trust paper

Added gradient clipping.

README.md

@@ -8,8 +8,12 @@ This implementation was transcribed from the official Tensorflow version <a href
 
 Youtube AI Educators - <a href="https://www.youtube.com/watch?v=W-O7AZNzbzQ">Yannic Kilcher</a> | <a href="https://www.youtube.com/watch?v=344w5h24-h8">AI Coffeebreak with Letitia</a> | <a href="https://www.youtube.com/watch?v=HoKDTa5jHvg">Outlier</a>
 
+<a href="https://github.com/yiyixuxu/denoising-diffusion-flax">Flax implementation</a> from <a href="https://github.com/yiyixuxu">YiYi Xu</a>
+
 <a href="https://huggingface.co/blog/annotated-diffusion">Annotated code</a> by Research Scientists / Engineers from <a href="https://huggingface.co/">🤗 Huggingface</a>
 
+Update: Turns out none of the technicalities really matters at all | <a href="https://arxiv.org/abs/2208.09392">"Cold Diffusion" paper</a>
+
 <img src="./images/sample.png" width="500px"><img>
 
 [![PyPI version](https://badge.fury.io/py/denoising-diffusion-pytorch.svg)](https://badge.fury.io/py/denoising-diffusion-pytorch)
@@ -38,7 +42,7 @@ diffusion = GaussianDiffusion(
     loss_type = 'l1'    # L1 or L2
 )
 
-training_images = torch.randn(8, 3, 128, 128) # images are normalized from 0 to 1
+training_images = torch.rand(8, 3, 128, 128) # images are normalized from 0 to 1
 loss = diffusion(training_images)
 loss.backward()
 # after a lot of training
@@ -97,6 +101,39 @@ Then, in the same directory
 $ accelerate launch train.py
 ```
 
+## Miscellaneous
+
+### 1D Sequence
+
+By popular request, a 1D Unet + Gaussian Diffusion implementation. You will have to do the training code yourself
+
+```python
+import torch
+from denoising_diffusion_pytorch import Unet1D, GaussianDiffusion1D
+
+model = Unet1D(
+    dim = 64,
+    dim_mults = (1, 2, 4, 8),
+    channels = 32
+)
+
+diffusion = GaussianDiffusion1D(
+    model,
+    seq_length = 128,
+    timesteps = 1000,
+    objective = 'pred_v'
+)
+
+training_seq = torch.rand(8, 32, 128) # features are normalized from 0 to 1
+loss = diffusion(training_seq)
+loss.backward()
+
+# after a lot of training
+
+sampled_seq = diffusion.sample(batch_size = 4)
+sampled_seq.shape # (4, 32, 128)
+```
+
 ## Citations
 
 ```bibtex
@@ -170,3 +207,54 @@ $ accelerate launch train.py
     volume  = {abs/2010.02502}
 }
 ```
+
+```bibtex
+@misc{chen2022analog,
+    title   = {Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning},
+    author  = {Ting Chen and Ruixiang Zhang and Geoffrey Hinton},
+    year    = {2022},
+    eprint  = {2208.04202},
+    archivePrefix = {arXiv},
+    primaryClass = {cs.CV}
+}
+```
+
+```bibtex
+@article{Qiao2019WeightS,
+    title   = {Weight Standardization},
+    author  = {Siyuan Qiao and Huiyu Wang and Chenxi Liu and Wei Shen and Alan Loddon Yuille},
+    journal = {ArXiv},
+    year    = {2019},
+    volume  = {abs/1903.10520}
+}
+```
+
+```bibtex
+@article{Salimans2022ProgressiveDF,
+    title   = {Progressive Distillation for Fast Sampling of Diffusion Models},
+    author  = {Tim Salimans and Jonathan Ho},
+    journal = {ArXiv},
+    year    = {2022},
+    volume  = {abs/2202.00512}
+}
+```
+
+```bibtex
+@article{Ho2022ClassifierFreeDG,
+    title   = {Classifier-Free Diffusion Guidance},
+    author  = {Jonathan Ho},
+    journal = {ArXiv},
+    year    = {2022},
+    volume  = {abs/2207.12598}
+}
+```
+
+```bibtex
+@article{Sunkara2022NoMS,
+    title   = {No More Strided Convolutions or Pooling: A New CNN Building Block for Low-Resolution Images and Small Objects},
+    author  = {Raja Sunkara and Tie Luo},
+    journal = {ArXiv},
+    year    = {2022},
+    volume  = {abs/2208.03641}
+}
+```

denoising_diffusion_pytorch/__init__.py

@@ -4,3 +4,7 @@ from denoising_diffusion_pytorch.learned_gaussian_diffusion import LearnedGaussi
 from denoising_diffusion_pytorch.continuous_time_gaussian_diffusion import ContinuousTimeGaussianDiffusion
 from denoising_diffusion_pytorch.weighted_objective_gaussian_diffusion import WeightedObjectiveGaussianDiffusion
 from denoising_diffusion_pytorch.elucidated_diffusion import ElucidatedDiffusion
+from denoising_diffusion_pytorch.v_param_continuous_time_gaussian_diffusion import VParamContinuousTimeGaussianDiffusion
+
+from denoising_diffusion_pytorch.denoising_diffusion_pytorch_1d import GaussianDiffusion1D, Unet1D
+

denoising_diffusion_pytorch/classifier_free_guidance.py

@@ -0,0 +1,792 @@
+import math
+import copy
+from pathlib import Path
+from random import random
+from functools import partial
+from collections import namedtuple
+from multiprocessing import cpu_count
+
+import torch
+from torch import nn, einsum
+import torch.nn.functional as F
+
+from einops import rearrange, reduce, repeat
+from einops.layers.torch import Rearrange
+
+from tqdm.auto import tqdm
+
+# constants
+
+ModelPrediction =  namedtuple('ModelPrediction', ['pred_noise', 'pred_x_start'])
+
+# helpers functions
+
+def exists(x):
+    return x is not None
+
+def default(val, d):
+    if exists(val):
+        return val
+    return d() if callable(d) else d
+
+def identity(t, *args, **kwargs):
+    return t
+
+def cycle(dl):
+    while True:
+        for data in dl:
+            yield data
+
+def has_int_squareroot(num):
+    return (math.sqrt(num) ** 2) == num
+
+def num_to_groups(num, divisor):
+    groups = num // divisor
+    remainder = num % divisor
+    arr = [divisor] * groups
+    if remainder > 0:
+        arr.append(remainder)
+    return arr
+
+def convert_image_to_fn(img_type, image):
+    if image.mode != img_type:
+        return image.convert(img_type)
+    return image
+
+# normalization functions
+
+def normalize_to_neg_one_to_one(img):
+    return img * 2 - 1
+
+def unnormalize_to_zero_to_one(t):
+    return (t + 1) * 0.5
+
+# classifier free guidance functions
+
+def uniform(shape, device):
+    return torch.zeros(shape, device = device).float().uniform_(0, 1)
+
+def prob_mask_like(shape, prob, device):
+    if prob == 1:
+        return torch.ones(shape, device = device, dtype = torch.bool)
+    elif prob == 0:
+        return torch.zeros(shape, device = device, dtype = torch.bool)
+    else:
+        return torch.zeros(shape, device = device).float().uniform_(0, 1) < prob
+
+# small helper modules
+
+class Residual(nn.Module):
+    def __init__(self, fn):
+        super().__init__()
+        self.fn = fn
+
+    def forward(self, x, *args, **kwargs):
+        return self.fn(x, *args, **kwargs) + x
+
+def Upsample(dim, dim_out = None):
+    return nn.Sequential(
+        nn.Upsample(scale_factor = 2, mode = 'nearest'),
+        nn.Conv2d(dim, default(dim_out, dim), 3, padding = 1)
+    )
+
+def Downsample(dim, dim_out = None):
+    return nn.Conv2d(dim, default(dim_out, dim), 4, 2, 1)
+
+class WeightStandardizedConv2d(nn.Conv2d):
+    """
+    https://arxiv.org/abs/1903.10520
+    weight standardization purportedly works synergistically with group normalization
+    """
+    def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
+
+        weight = self.weight
+        mean = reduce(weight, 'o ... -> o 1 1 1', 'mean')
+        var = reduce(weight, 'o ... -> o 1 1 1', partial(torch.var, unbiased = False))
+        normalized_weight = (weight - mean) * (var + eps).rsqrt()
+
+        return F.conv2d(x, normalized_weight, self.bias, self.stride, self.padding, self.dilation, self.groups)
+
+class LayerNorm(nn.Module):
+    def __init__(self, dim):
+        super().__init__()
+        self.g = nn.Parameter(torch.ones(1, dim, 1, 1))
+
+    def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
+        var = torch.var(x, dim = 1, unbiased = False, keepdim = True)
+        mean = torch.mean(x, dim = 1, keepdim = True)
+        return (x - mean) * (var + eps).rsqrt() * self.g
+
+class PreNorm(nn.Module):
+    def __init__(self, dim, fn):
+        super().__init__()
+        self.fn = fn
+        self.norm = LayerNorm(dim)
+
+    def forward(self, x):
+        x = self.norm(x)
+        return self.fn(x)
+
+# sinusoidal positional embeds
+
+class SinusoidalPosEmb(nn.Module):
+    def __init__(self, dim):
+        super().__init__()
+        self.dim = dim
+
+    def forward(self, x):
+        device = x.device
+        half_dim = self.dim // 2
+        emb = math.log(10000) / (half_dim - 1)
+        emb = torch.exp(torch.arange(half_dim, device=device) * -emb)
+        emb = x[:, None] * emb[None, :]
+        emb = torch.cat((emb.sin(), emb.cos()), dim=-1)
+        return emb
+
+class RandomOrLearnedSinusoidalPosEmb(nn.Module):
+    """ following @crowsonkb 's lead with random (learned optional) sinusoidal pos emb """
+    """ https://github.com/crowsonkb/v-diffusion-jax/blob/master/diffusion/models/danbooru_128.py#L8 """
+
+    def __init__(self, dim, is_random = False):
+        super().__init__()
+        assert (dim % 2) == 0
+        half_dim = dim // 2
+        self.weights = nn.Parameter(torch.randn(half_dim), requires_grad = not is_random)
+
+    def forward(self, x):
+        x = rearrange(x, 'b -> b 1')
+        freqs = x * rearrange(self.weights, 'd -> 1 d') * 2 * math.pi
+        fouriered = torch.cat((freqs.sin(), freqs.cos()), dim = -1)
+        fouriered = torch.cat((x, fouriered), dim = -1)
+        return fouriered
+
+# building block modules
+
+class Block(nn.Module):
+    def __init__(self, dim, dim_out, groups = 8):
+        super().__init__()
+        self.proj = WeightStandardizedConv2d(dim, dim_out, 3, padding = 1)
+        self.norm = nn.GroupNorm(groups, dim_out)
+        self.act = nn.SiLU()
+
+    def forward(self, x, scale_shift = None):
+        x = self.proj(x)
+        x = self.norm(x)
+
+        if exists(scale_shift):
+            scale, shift = scale_shift
+            x = x * (scale + 1) + shift
+
+        x = self.act(x)
+        return x
+
+class ResnetBlock(nn.Module):
+    def __init__(self, dim, dim_out, *, time_emb_dim = None, classes_emb_dim = None, groups = 8):
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.SiLU(),
+            nn.Linear(int(time_emb_dim) + int(classes_emb_dim), dim_out * 2)
+        ) if exists(time_emb_dim) or exists(classes_emb_dim) else None
+
+        self.block1 = Block(dim, dim_out, groups = groups)
+        self.block2 = Block(dim_out, dim_out, groups = groups)
+        self.res_conv = nn.Conv2d(dim, dim_out, 1) if dim != dim_out else nn.Identity()
+
+    def forward(self, x, time_emb = None, class_emb = None):
+
+        scale_shift = None
+        if exists(self.mlp) and (exists(time_emb) or exists(class_emb)):
+            cond_emb = tuple(filter(exists, (time_emb, class_emb)))
+            cond_emb = torch.cat(cond_emb, dim = -1)
+            cond_emb = self.mlp(cond_emb)
+            cond_emb = rearrange(cond_emb, 'b c -> b c 1 1')
+            scale_shift = cond_emb.chunk(2, dim = 1)
+
+        h = self.block1(x, scale_shift = scale_shift)
+
+        h = self.block2(h)
+
+        return h + self.res_conv(x)
+
+class LinearAttention(nn.Module):
+    def __init__(self, dim, heads = 4, dim_head = 32):
+        super().__init__()
+        self.scale = dim_head ** -0.5
+        self.heads = heads
+        hidden_dim = dim_head * heads
+        self.to_qkv = nn.Conv2d(dim, hidden_dim * 3, 1, bias = False)
+
+        self.to_out = nn.Sequential(
+            nn.Conv2d(hidden_dim, dim, 1),
+            LayerNorm(dim)
+        )
+
+    def forward(self, x):
+        b, c, h, w = x.shape
+        qkv = self.to_qkv(x).chunk(3, dim = 1)
+        q, k, v = map(lambda t: rearrange(t, 'b (h c) x y -> b h c (x y)', h = self.heads), qkv)
+
+        q = q.softmax(dim = -2)
+        k = k.softmax(dim = -1)
+
+        q = q * self.scale
+        v = v / (h * w)
+
+        context = torch.einsum('b h d n, b h e n -> b h d e', k, v)
+
+        out = torch.einsum('b h d e, b h d n -> b h e n', context, q)
+        out = rearrange(out, 'b h c (x y) -> b (h c) x y', h = self.heads, x = h, y = w)
+        return self.to_out(out)
+
+class Attention(nn.Module):
+    def __init__(self, dim, heads = 4, dim_head = 32):
+        super().__init__()
+        self.scale = dim_head ** -0.5
+        self.heads = heads
+        hidden_dim = dim_head * heads
+
+        self.to_qkv = nn.Conv2d(dim, hidden_dim * 3, 1, bias = False)
+        self.to_out = nn.Conv2d(hidden_dim, dim, 1)
+
+    def forward(self, x):
+        b, c, h, w = x.shape
+        qkv = self.to_qkv(x).chunk(3, dim = 1)
+        q, k, v = map(lambda t: rearrange(t, 'b (h c) x y -> b h c (x y)', h = self.heads), qkv)
+
+        q = q * self.scale
+
+        sim = einsum('b h d i, b h d j -> b h i j', q, k)
+        attn = sim.softmax(dim = -1)
+        out = einsum('b h i j, b h d j -> b h i d', attn, v)
+
+        out = rearrange(out, 'b h (x y) d -> b (h d) x y', x = h, y = w)
+        return self.to_out(out)
+
+# model
+
+class Unet(nn.Module):
+    def __init__(
+        self,
+        dim,
+        num_classes,
+        cond_drop_prob = 0.5,
+        init_dim = None,
+        out_dim = None,
+        dim_mults=(1, 2, 4, 8),
+        channels = 3,
+        resnet_block_groups = 8,
+        learned_variance = False,
+        learned_sinusoidal_cond = False,
+        random_fourier_features = False,
+        learned_sinusoidal_dim = 16,
+    ):
+        super().__init__()
+
+        # classifier free guidance stuff
+
+        self.cond_drop_prob = cond_drop_prob
+
+        # determine dimensions
+
+        self.channels = channels
+        input_channels = channels
+
+        init_dim = default(init_dim, dim)
+        self.init_conv = nn.Conv2d(input_channels, init_dim, 7, padding = 3)
+
+        dims = [init_dim, *map(lambda m: dim * m, dim_mults)]
+        in_out = list(zip(dims[:-1], dims[1:]))
+
+        block_klass = partial(ResnetBlock, groups = resnet_block_groups)
+
+        # time embeddings
+
+        time_dim = dim * 4
+
+        self.random_or_learned_sinusoidal_cond = learned_sinusoidal_cond or random_fourier_features
+
+        if self.random_or_learned_sinusoidal_cond:
+            sinu_pos_emb = RandomOrLearnedSinusoidalPosEmb(learned_sinusoidal_dim, random_fourier_features)
+            fourier_dim = learned_sinusoidal_dim + 1
+        else:
+            sinu_pos_emb = SinusoidalPosEmb(dim)
+            fourier_dim = dim
+
+        self.time_mlp = nn.Sequential(
+            sinu_pos_emb,
+            nn.Linear(fourier_dim, time_dim),
+            nn.GELU(),
+            nn.Linear(time_dim, time_dim)
+        )
+
+        # class embeddings
+
+        self.classes_emb = nn.Embedding(num_classes, dim)
+        self.null_classes_emb = nn.Parameter(torch.randn(dim))
+
+        classes_dim = dim * 4
+
+        self.classes_mlp = nn.Sequential(
+            nn.Linear(dim, classes_dim),
+            nn.GELU(),
+            nn.Linear(classes_dim, classes_dim)
+        )
+
+        # layers
+
+        self.downs = nn.ModuleList([])
+        self.ups = nn.ModuleList([])
+        num_resolutions = len(in_out)
+
+        for ind, (dim_in, dim_out) in enumerate(in_out):
+            is_last = ind >= (num_resolutions - 1)
+
+            self.downs.append(nn.ModuleList([
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim, classes_emb_dim = classes_dim),
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim, classes_emb_dim = classes_dim),
+                Residual(PreNorm(dim_in, LinearAttention(dim_in))),
+                Downsample(dim_in, dim_out) if not is_last else nn.Conv2d(dim_in, dim_out, 3, padding = 1)
+            ]))
+
+        mid_dim = dims[-1]
+        self.mid_block1 = block_klass(mid_dim, mid_dim, time_emb_dim = time_dim, classes_emb_dim = classes_dim)
+        self.mid_attn = Residual(PreNorm(mid_dim, Attention(mid_dim)))
+        self.mid_block2 = block_klass(mid_dim, mid_dim, time_emb_dim = time_dim, classes_emb_dim = classes_dim)
+
+        for ind, (dim_in, dim_out) in enumerate(reversed(in_out)):
+            is_last = ind == (len(in_out) - 1)
+
+            self.ups.append(nn.ModuleList([
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim, classes_emb_dim = classes_dim),
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim, classes_emb_dim = classes_dim),
+                Residual(PreNorm(dim_out, LinearAttention(dim_out))),
+                Upsample(dim_out, dim_in) if not is_last else  nn.Conv2d(dim_out, dim_in, 3, padding = 1)
+            ]))
+
+        default_out_dim = channels * (1 if not learned_variance else 2)
+        self.out_dim = default(out_dim, default_out_dim)
+
+        self.final_res_block = block_klass(dim * 2, dim, time_emb_dim = time_dim, classes_emb_dim = classes_dim)
+        self.final_conv = nn.Conv2d(dim, self.out_dim, 1)
+
+    def forward_with_cond_scale(
+        self,
+        *args,
+        cond_scale = 1.,
+        **kwargs
+    ):
+        logits = self.forward(*args, **kwargs)
+
+        if cond_scale == 1:
+            return logits
+
+        null_logits = self.forward(*args, cond_drop_prob = 1., **kwargs)
+        return null_logits + (logits - null_logits) * cond_scale
+
+    def forward(
+        self,
+        x,
+        time,
+        classes,
+        cond_drop_prob = None
+    ):
+        batch, device = x.shape[0], x.device
+
+        cond_drop_prob = default(cond_drop_prob, self.cond_drop_prob)
+
+        # derive condition, with condition dropout for classifier free guidance        
+
+        classes_emb = self.classes_emb(classes)
+
+        if cond_drop_prob > 0:
+            keep_mask = prob_mask_like((batch,), 1 - cond_drop_prob, device = device)
+            null_classes_emb = repeat(self.null_classes_emb, 'd -> b d', b = batch)
+
+            classes_emb = torch.where(
+                rearrange(keep_mask, 'b -> b 1'),
+                classes_emb,
+                null_classes_emb
+            )
+
+        c = self.classes_mlp(classes_emb)
+
+        # unet
+
+        x = self.init_conv(x)
+        r = x.clone()
+
+        t = self.time_mlp(time)
+
+        h = []
+
+        for block1, block2, attn, downsample in self.downs:
+            x = block1(x, t, c)
+            h.append(x)
+
+            x = block2(x, t, c)
+            x = attn(x)
+            h.append(x)
+
+            x = downsample(x)
+
+        x = self.mid_block1(x, t, c)
+        x = self.mid_attn(x)
+        x = self.mid_block2(x, t, c)
+
+        for block1, block2, attn, upsample in self.ups:
+            x = torch.cat((x, h.pop()), dim = 1)
+            x = block1(x, t, c)
+
+            x = torch.cat((x, h.pop()), dim = 1)
+            x = block2(x, t, c)
+            x = attn(x)
+
+            x = upsample(x)
+
+        x = torch.cat((x, r), dim = 1)
+
+        x = self.final_res_block(x, t, c)
+        return self.final_conv(x)
+
+# gaussian diffusion trainer class
+
+def extract(a, t, x_shape):
+    b, *_ = t.shape
+    out = a.gather(-1, t)
+    return out.reshape(b, *((1,) * (len(x_shape) - 1)))
+
+def linear_beta_schedule(timesteps):
+    scale = 1000 / timesteps
+    beta_start = scale * 0.0001
+    beta_end = scale * 0.02
+    return torch.linspace(beta_start, beta_end, timesteps, dtype = torch.float64)
+
+def cosine_beta_schedule(timesteps, s = 0.008):
+    """
+    cosine schedule
+    as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
+    """
+    steps = timesteps + 1
+    x = torch.linspace(0, timesteps, steps, dtype = torch.float64)
+    alphas_cumprod = torch.cos(((x / timesteps) + s) / (1 + s) * math.pi * 0.5) ** 2
+    alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
+    betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
+    return torch.clip(betas, 0, 0.999)
+
+class GaussianDiffusion(nn.Module):
+    def __init__(
+        self,
+        model,
+        *,
+        image_size,
+        timesteps = 1000,
+        sampling_timesteps = None,
+        loss_type = 'l1',
+        objective = 'pred_noise',
+        beta_schedule = 'cosine',
+        p2_loss_weight_gamma = 0., # p2 loss weight, from https://arxiv.org/abs/2204.00227 - 0 is equivalent to weight of 1 across time - 1. is recommended
+        p2_loss_weight_k = 1,
+        ddim_sampling_eta = 1.
+    ):
+        super().__init__()
+        assert not (type(self) == GaussianDiffusion and model.channels != model.out_dim)
+        assert not model.random_or_learned_sinusoidal_cond
+
+        self.model = model
+        self.channels = self.model.channels
+
+        self.image_size = image_size
+
+        self.objective = objective
+
+        assert objective in {'pred_noise', 'pred_x0', 'pred_v'}, 'objective must be either pred_noise (predict noise) or pred_x0 (predict image start) or pred_v (predict v [v-parameterization as defined in appendix D of progressive distillation paper, used in imagen-video successfully])'
+
+        if beta_schedule == 'linear':
+            betas = linear_beta_schedule(timesteps)
+        elif beta_schedule == 'cosine':
+            betas = cosine_beta_schedule(timesteps)
+        else:
+            raise ValueError(f'unknown beta schedule {beta_schedule}')
+
+        alphas = 1. - betas
+        alphas_cumprod = torch.cumprod(alphas, dim=0)
+        alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value = 1.)
+
+        timesteps, = betas.shape
+        self.num_timesteps = int(timesteps)
+        self.loss_type = loss_type
+
+        # sampling related parameters
+
+        self.sampling_timesteps = default(sampling_timesteps, timesteps) # default num sampling timesteps to number of timesteps at training
+
+        assert self.sampling_timesteps <= timesteps
+        self.is_ddim_sampling = self.sampling_timesteps < timesteps
+        self.ddim_sampling_eta = ddim_sampling_eta
+
+        # helper function to register buffer from float64 to float32
+
+        register_buffer = lambda name, val: self.register_buffer(name, val.to(torch.float32))
+
+        register_buffer('betas', betas)
+        register_buffer('alphas_cumprod', alphas_cumprod)
+        register_buffer('alphas_cumprod_prev', alphas_cumprod_prev)
+
+        # calculations for diffusion q(x_t | x_{t-1}) and others
+
+        register_buffer('sqrt_alphas_cumprod', torch.sqrt(alphas_cumprod))
+        register_buffer('sqrt_one_minus_alphas_cumprod', torch.sqrt(1. - alphas_cumprod))
+        register_buffer('log_one_minus_alphas_cumprod', torch.log(1. - alphas_cumprod))
+        register_buffer('sqrt_recip_alphas_cumprod', torch.sqrt(1. / alphas_cumprod))
+        register_buffer('sqrt_recipm1_alphas_cumprod', torch.sqrt(1. / alphas_cumprod - 1))
+
+        # calculations for posterior q(x_{t-1} | x_t, x_0)
+
+        posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod)
+
+        # above: equal to 1. / (1. / (1. - alpha_cumprod_tm1) + alpha_t / beta_t)
+
+        register_buffer('posterior_variance', posterior_variance)
+
+        # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain
+
+        register_buffer('posterior_log_variance_clipped', torch.log(posterior_variance.clamp(min =1e-20)))
+        register_buffer('posterior_mean_coef1', betas * torch.sqrt(alphas_cumprod_prev) / (1. - alphas_cumprod))
+        register_buffer('posterior_mean_coef2', (1. - alphas_cumprod_prev) * torch.sqrt(alphas) / (1. - alphas_cumprod))
+
+        # calculate p2 reweighting
+
+        register_buffer('p2_loss_weight', (p2_loss_weight_k + alphas_cumprod / (1 - alphas_cumprod)) ** -p2_loss_weight_gamma)
+
+    def predict_start_from_noise(self, x_t, t, noise):
+        return (
+            extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * noise
+        )
+
+    def predict_noise_from_start(self, x_t, t, x0):
+        return (
+            (extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - x0) / \
+            extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
+        )
+
+    def predict_v(self, x_start, t, noise):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * noise -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * x_start
+        )
+
+    def predict_start_from_v(self, x_t, t, v):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_t.shape) * v
+        )
+
+    def q_posterior(self, x_start, x_t, t):
+        posterior_mean = (
+            extract(self.posterior_mean_coef1, t, x_t.shape) * x_start +
+            extract(self.posterior_mean_coef2, t, x_t.shape) * x_t
+        )
+        posterior_variance = extract(self.posterior_variance, t, x_t.shape)
+        posterior_log_variance_clipped = extract(self.posterior_log_variance_clipped, t, x_t.shape)
+        return posterior_mean, posterior_variance, posterior_log_variance_clipped
+
+    def model_predictions(self, x, t, classes, cond_scale = 3., clip_x_start = False):
+        model_output = self.model.forward_with_cond_scale(x, t, classes, cond_scale = cond_scale)
+        maybe_clip = partial(torch.clamp, min = -1., max = 1.) if clip_x_start else identity
+
+        if self.objective == 'pred_noise':
+            pred_noise = model_output
+            x_start = self.predict_start_from_noise(x, t, pred_noise)
+            x_start = maybe_clip(x_start)
+
+        elif self.objective == 'pred_x0':
+            x_start = model_output
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
+        elif self.objective == 'pred_v':
+            v = model_output
+            x_start = self.predict_start_from_v(x, t, v)
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
+        return ModelPrediction(pred_noise, x_start)
+
+    def p_mean_variance(self, x, t, classes, cond_scale, clip_denoised = True):
+        preds = self.model_predictions(x, t, classes, cond_scale)
+        x_start = preds.pred_x_start
+
+        if clip_denoised:
+            x_start.clamp_(-1., 1.)
+
+        model_mean, posterior_variance, posterior_log_variance = self.q_posterior(x_start = x_start, x_t = x, t = t)
+        return model_mean, posterior_variance, posterior_log_variance, x_start
+
+    @torch.no_grad()
+    def p_sample(self, x, t: int, classes, cond_scale = 3., clip_denoised = True):
+        b, *_, device = *x.shape, x.device
+        batched_times = torch.full((x.shape[0],), t, device = x.device, dtype = torch.long)
+        model_mean, _, model_log_variance, x_start = self.p_mean_variance(x = x, t = batched_times, classes = classes, cond_scale = cond_scale, clip_denoised = clip_denoised)
+        noise = torch.randn_like(x) if t > 0 else 0. # no noise if t == 0
+        pred_img = model_mean + (0.5 * model_log_variance).exp() * noise
+        return pred_img, x_start
+
+    @torch.no_grad()
+    def p_sample_loop(self, classes, shape, cond_scale = 3.):
+        batch, device = shape[0], self.betas.device
+
+        img = torch.randn(shape, device=device)
+
+        x_start = None
+
+        for t in tqdm(reversed(range(0, self.num_timesteps)), desc = 'sampling loop time step', total = self.num_timesteps):
+            img, x_start = self.p_sample(img, t, classes, cond_scale)
+
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def ddim_sample(self, classes, shape, cond_scale = 3., clip_denoised = True):
+        batch, device, total_timesteps, sampling_timesteps, eta, objective = shape[0], self.betas.device, self.num_timesteps, self.sampling_timesteps, self.ddim_sampling_eta, self.objective
+
+        times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1)   # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps
+        times = list(reversed(times.int().tolist()))
+        time_pairs = list(zip(times[:-1], times[1:])) # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)]
+
+        img = torch.randn(shape, device = device)
+
+        x_start = None
+
+        for time, time_next in tqdm(time_pairs, desc = 'sampling loop time step'):
+            time_cond = torch.full((batch,), time, device=device, dtype=torch.long)
+            pred_noise, x_start, *_ = self.model_predictions(img, time_cond, classes, cond_scale = cond_scale, clip_x_start = clip_denoised)
+
+            if time_next < 0:
+                img = x_start
+                continue
+
+            alpha = self.alphas_cumprod[time]
+            alpha_next = self.alphas_cumprod[time_next]
+
+            sigma = eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt()
+            c = (1 - alpha_next - sigma ** 2).sqrt()
+
+            noise = torch.randn_like(img)
+
+            img = x_start * alpha_next.sqrt() + \
+                  c * pred_noise + \
+                  sigma * noise
+
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def sample(self, classes, cond_scale = 3.):
+        batch_size, image_size, channels = classes.shape[0], self.image_size, self.channels
+        sample_fn = self.p_sample_loop if not self.is_ddim_sampling else self.ddim_sample
+        return sample_fn(classes, (batch_size, channels, image_size, image_size), cond_scale)
+
+    @torch.no_grad()
+    def interpolate(self, x1, x2, t = None, lam = 0.5):
+        b, *_, device = *x1.shape, x1.device
+        t = default(t, self.num_timesteps - 1)
+
+        assert x1.shape == x2.shape
+
+        t_batched = torch.stack([torch.tensor(t, device = device)] * b)
+        xt1, xt2 = map(lambda x: self.q_sample(x, t = t_batched), (x1, x2))
+
+        img = (1 - lam) * xt1 + lam * xt2
+        for i in tqdm(reversed(range(0, t)), desc = 'interpolation sample time step', total = t):
+            img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))
+
+        return img
+
+    def q_sample(self, x_start, t, noise=None):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start +
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise
+        )
+
+    @property
+    def loss_fn(self):
+        if self.loss_type == 'l1':
+            return F.l1_loss
+        elif self.loss_type == 'l2':
+            return F.mse_loss
+        else:
+            raise ValueError(f'invalid loss type {self.loss_type}')
+
+    def p_losses(self, x_start, t, *, classes, noise = None):
+        b, c, h, w = x_start.shape
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        # noise sample
+
+        x = self.q_sample(x_start = x_start, t = t, noise = noise)
+
+        # predict and take gradient step
+
+        model_out = self.model(x, t, classes)
+
+        if self.objective == 'pred_noise':
+            target = noise
+        elif self.objective == 'pred_x0':
+            target = x_start
+        elif self.objective == 'pred_v':
+            v = self.predict_v(x_start, t, noise)
+            target = v
+        else:
+            raise ValueError(f'unknown objective {self.objective}')
+
+        loss = self.loss_fn(model_out, target, reduction = 'none')
+        loss = reduce(loss, 'b ... -> b (...)', 'mean')
+
+        loss = loss * extract(self.p2_loss_weight, t, loss.shape)
+        return loss.mean()
+
+    def forward(self, img, *args, **kwargs):
+        b, c, h, w, device, img_size, = *img.shape, img.device, self.image_size
+        assert h == img_size and w == img_size, f'height and width of image must be {img_size}'
+        t = torch.randint(0, self.num_timesteps, (b,), device=device).long()
+
+        img = normalize_to_neg_one_to_one(img)
+        return self.p_losses(img, t, *args, **kwargs)
+
+# example
+
+if __name__ == '__main__':
+    num_classes = 10
+
+    model = Unet(
+        dim = 64,
+        dim_mults = (1, 2, 4, 8),
+        num_classes = num_classes,
+        cond_drop_prob = 0.5
+    )
+
+    diffusion = GaussianDiffusion(
+        model,
+        image_size = 128,
+        timesteps = 1000
+    ).cuda()
+
+    training_images = torch.randn(8, 3, 128, 128).cuda() # images are normalized from 0 to 1
+    image_classes = torch.randint(0, num_classes, (8,)).cuda()    # say 10 classes
+
+    loss = diffusion(training_images, classes = image_classes)
+    loss.backward()
+
+    # do above for many steps
+
+    sampled_images = diffusion.sample(
+        classes = image_classes,
+        cond_scale = 3.                # condition scaling, anything greater than 1 strengthens the classifier free guidance. reportedly 3-8 is good empirically
+    )
+
+    sampled_images.shape # (8, 3, 128, 128)

denoising_diffusion_pytorch/continuous_time_gaussian_diffusion.py

@@ -126,7 +126,8 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         p2_loss_weight_k = 1
     ):
         super().__init__()
-        assert model.learned_sinusoidal_cond
+        assert model.random_or_learned_sinusoidal_cond
+        assert not model.self_condition, 'not supported yet'
 
         self.model = model
 

denoising_diffusion_pytorch/denoising_diffusion_pytorch.py

@@ -1,23 +1,23 @@
 import math
 import copy
+from pathlib import Path
+from random import random
+from functools import partial
+from collections import namedtuple
+from multiprocessing import cpu_count
+
 import torch
 from torch import nn, einsum
 import torch.nn.functional as F
-from inspect import isfunction
-from collections import namedtuple
-from functools import partial
-
 from torch.utils.data import Dataset, DataLoader
-from multiprocessing import cpu_count
 
-from pathlib import Path
 from torch.optim import Adam
 from torchvision import transforms as T, utils
-from PIL import Image
 
 from einops import rearrange, reduce
 from einops.layers.torch import Rearrange
 
+from PIL import Image
 from tqdm.auto import tqdm
 from ema_pytorch import EMA
 
@@ -35,7 +35,10 @@ def exists(x):
 def default(val, d):
     if exists(val):
         return val
-    return d() if isfunction(d) else d
+    return d() if callable(d) else d
+
+def identity(t, *args, **kwargs):
+    return t
 
 def cycle(dl):
     while True:
@@ -53,14 +56,11 @@ def num_to_groups(num, divisor):
         arr.append(remainder)
     return arr
 
-def convert_image_to(img_type, image):
+def convert_image_to_fn(img_type, image):
     if image.mode != img_type:
         return image.convert(img_type)
     return image
 
-def l2norm(t):
-    return F.normalize(t, dim = -1)
-
 # normalization functions
 
 def normalize_to_neg_one_to_one(img):
@@ -86,19 +86,36 @@ def Upsample(dim, dim_out = None):
     )
 
 def Downsample(dim, dim_out = None):
-    return nn.Conv2d(dim, default(dim_out, dim), 4, 2, 1)
+    return nn.Sequential(
+        Rearrange('b c (h p1) (w p2) -> b (c p1 p2) h w', p1 = 2, p2 = 2),
+        nn.Conv2d(dim * 4, default(dim_out, dim), 1)
+    )
+
+class WeightStandardizedConv2d(nn.Conv2d):
+    """
+    https://arxiv.org/abs/1903.10520
+    weight standardization purportedly works synergistically with group normalization
+    """
+    def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
+
+        weight = self.weight
+        mean = reduce(weight, 'o ... -> o 1 1 1', 'mean')
+        var = reduce(weight, 'o ... -> o 1 1 1', partial(torch.var, unbiased = False))
+        normalized_weight = (weight - mean) * (var + eps).rsqrt()
+
+        return F.conv2d(x, normalized_weight, self.bias, self.stride, self.padding, self.dilation, self.groups)
 
 class LayerNorm(nn.Module):
-    def __init__(self, dim, eps = 1e-5):
+    def __init__(self, dim):
         super().__init__()
-        self.eps = eps
         self.g = nn.Parameter(torch.ones(1, dim, 1, 1))
-        self.b = nn.Parameter(torch.zeros(1, dim, 1, 1))
 
     def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
         var = torch.var(x, dim = 1, unbiased = False, keepdim = True)
         mean = torch.mean(x, dim = 1, keepdim = True)
-        return (x - mean) / (var + self.eps).sqrt() * self.g + self.b
+        return (x - mean) * (var + eps).rsqrt() * self.g
 
 class PreNorm(nn.Module):
     def __init__(self, dim, fn):
@@ -126,15 +143,15 @@ class SinusoidalPosEmb(nn.Module):
         emb = torch.cat((emb.sin(), emb.cos()), dim=-1)
         return emb
 
-class LearnedSinusoidalPosEmb(nn.Module):
+class RandomOrLearnedSinusoidalPosEmb(nn.Module):
-    """ following @crowsonkb 's lead with learned sinusoidal pos emb """
+    """ following @crowsonkb 's lead with random (learned optional) sinusoidal pos emb """
     """ https://github.com/crowsonkb/v-diffusion-jax/blob/master/diffusion/models/danbooru_128.py#L8 """
 
-    def __init__(self, dim):
+    def __init__(self, dim, is_random = False):
         super().__init__()
         assert (dim % 2) == 0
         half_dim = dim // 2
-        self.weights = nn.Parameter(torch.randn(half_dim))
+        self.weights = nn.Parameter(torch.randn(half_dim), requires_grad = not is_random)
 
     def forward(self, x):
         x = rearrange(x, 'b -> b 1')
@@ -148,7 +165,7 @@ class LearnedSinusoidalPosEmb(nn.Module):
 class Block(nn.Module):
     def __init__(self, dim, dim_out, groups = 8):
         super().__init__()
-        self.proj = nn.Conv2d(dim, dim_out, 3, padding = 1)
+        self.proj = WeightStandardizedConv2d(dim, dim_out, 3, padding = 1)
         self.norm = nn.GroupNorm(groups, dim_out)
         self.act = nn.SiLU()
 
@@ -220,11 +237,12 @@ class LinearAttention(nn.Module):
         return self.to_out(out)
 
 class Attention(nn.Module):
-    def __init__(self, dim, heads = 4, dim_head = 32, scale = 16):
+    def __init__(self, dim, heads = 4, dim_head = 32):
         super().__init__()
-        self.scale = scale
+        self.scale = dim_head ** -0.5
         self.heads = heads
         hidden_dim = dim_head * heads
+
         self.to_qkv = nn.Conv2d(dim, hidden_dim * 3, 1, bias = False)
         self.to_out = nn.Conv2d(hidden_dim, dim, 1)
 
@@ -233,12 +251,12 @@ class Attention(nn.Module):
         qkv = self.to_qkv(x).chunk(3, dim = 1)
         q, k, v = map(lambda t: rearrange(t, 'b (h c) x y -> b h c (x y)', h = self.heads), qkv)
 
-        q, k = map(l2norm, (q, k))
+        q = q * self.scale
 
-        sim = einsum('b h d i, b h d j -> b h i j', q, k) * self.scale
+        sim = einsum('b h d i, b h d j -> b h i j', q, k)
         attn = sim.softmax(dim = -1)
-
         out = einsum('b h i j, b h d j -> b h i d', attn, v)
+
         out = rearrange(out, 'b h (x y) d -> b (h d) x y', x = h, y = w)
         return self.to_out(out)
 
@@ -252,9 +270,11 @@ class Unet(nn.Module):
         out_dim = None,
         dim_mults=(1, 2, 4, 8),
         channels = 3,
+        self_condition = False,
         resnet_block_groups = 8,
         learned_variance = False,
         learned_sinusoidal_cond = False,
+        random_fourier_features = False,
         learned_sinusoidal_dim = 16
     ):
         super().__init__()
@@ -262,9 +282,11 @@ class Unet(nn.Module):
         # determine dimensions
 
         self.channels = channels
+        self.self_condition = self_condition
+        input_channels = channels * (2 if self_condition else 1)
 
         init_dim = default(init_dim, dim)
-        self.init_conv = nn.Conv2d(channels, init_dim, 7, padding = 3)
+        self.init_conv = nn.Conv2d(input_channels, init_dim, 7, padding = 3)
 
         dims = [init_dim, *map(lambda m: dim * m, dim_mults)]
         in_out = list(zip(dims[:-1], dims[1:]))
@@ -275,10 +297,10 @@ class Unet(nn.Module):
 
         time_dim = dim * 4
 
-        self.learned_sinusoidal_cond = learned_sinusoidal_cond
+        self.random_or_learned_sinusoidal_cond = learned_sinusoidal_cond or random_fourier_features
 
-        if learned_sinusoidal_cond:
+        if self.random_or_learned_sinusoidal_cond:
-            sinu_pos_emb = LearnedSinusoidalPosEmb(learned_sinusoidal_dim)
+            sinu_pos_emb = RandomOrLearnedSinusoidalPosEmb(learned_sinusoidal_dim, random_fourier_features)
             fourier_dim = learned_sinusoidal_dim + 1
         else:
             sinu_pos_emb = SinusoidalPosEmb(dim)
@@ -328,7 +350,11 @@ class Unet(nn.Module):
         self.final_res_block = block_klass(dim * 2, dim, time_emb_dim = time_dim)
         self.final_conv = nn.Conv2d(dim, self.out_dim, 1)
 
-    def forward(self, x, time):
+    def forward(self, x, time, x_self_cond = None):
+        if self.self_condition:
+            x_self_cond = default(x_self_cond, lambda: torch.zeros_like(x))
+            x = torch.cat((x_self_cond, x), dim = 1)
+
         x = self.init_conv(x)
         r = x.clone()
 
@@ -396,7 +422,6 @@ class GaussianDiffusion(nn.Module):
         model,
         *,
         image_size,
-        channels = 3,
         timesteps = 1000,
         sampling_timesteps = None,
         loss_type = 'l1',
@@ -408,13 +433,17 @@ class GaussianDiffusion(nn.Module):
     ):
         super().__init__()
         assert not (type(self) == GaussianDiffusion and model.channels != model.out_dim)
+        assert not model.random_or_learned_sinusoidal_cond
 
-        self.channels = channels
-        self.image_size = image_size
         self.model = model
+        self.channels = self.model.channels
+        self.self_condition = self.model.self_condition
+
+        self.image_size = image_size
+
         self.objective = objective
 
-        assert objective in {'pred_noise', 'pred_x0'}, 'objective must be either pred_noise (predict noise) or pred_x0 (predict image start)'
+        assert objective in {'pred_noise', 'pred_x0', 'pred_v'}, 'objective must be either pred_noise (predict noise) or pred_x0 (predict image start) or pred_v (predict v [v-parameterization as defined in appendix D of progressive distillation paper, used in imagen-video successfully])'
 
         if beta_schedule == 'linear':
             betas = linear_beta_schedule(timesteps)
@@ -424,7 +453,7 @@ class GaussianDiffusion(nn.Module):
             raise ValueError(f'unknown beta schedule {beta_schedule}')
 
         alphas = 1. - betas
-        alphas_cumprod = torch.cumprod(alphas, axis=0)
+        alphas_cumprod = torch.cumprod(alphas, dim=0)
         alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value = 1.)
 
         timesteps, = betas.shape
@@ -485,6 +514,18 @@ class GaussianDiffusion(nn.Module):
             extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
         )
 
+    def predict_v(self, x_start, t, noise):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * noise -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * x_start
+        )
+
+    def predict_start_from_v(self, x_t, t, v):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_t.shape) * v
+        )
+
     def q_posterior(self, x_start, x_t, t):
         posterior_mean = (
             extract(self.posterior_mean_coef1, t, x_t.shape) * x_start +
@@ -494,36 +535,46 @@ class GaussianDiffusion(nn.Module):
         posterior_log_variance_clipped = extract(self.posterior_log_variance_clipped, t, x_t.shape)
         return posterior_mean, posterior_variance, posterior_log_variance_clipped
 
-    def model_predictions(self, x, t):
+    def model_predictions(self, x, t, x_self_cond = None, clip_x_start = False):
-        model_output = self.model(x, t)
+        model_output = self.model(x, t, x_self_cond)
+        maybe_clip = partial(torch.clamp, min = -1., max = 1.) if clip_x_start else identity
 
         if self.objective == 'pred_noise':
             pred_noise = model_output
-            x_start = self.predict_start_from_noise(x, t, model_output)
+            x_start = self.predict_start_from_noise(x, t, pred_noise)
+            x_start = maybe_clip(x_start)
 
         elif self.objective == 'pred_x0':
-            pred_noise = self.predict_noise_from_start(x, t, model_output)
             x_start = model_output
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
+        elif self.objective == 'pred_v':
+            v = model_output
+            x_start = self.predict_start_from_v(x, t, v)
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
 
         return ModelPrediction(pred_noise, x_start)
 
-    def p_mean_variance(self, x, t, clip_denoised: bool):
+    def p_mean_variance(self, x, t, x_self_cond = None, clip_denoised = True):
-        preds = self.model_predictions(x, t)
+        preds = self.model_predictions(x, t, x_self_cond)
         x_start = preds.pred_x_start
 
         if clip_denoised:
             x_start.clamp_(-1., 1.)
 
         model_mean, posterior_variance, posterior_log_variance = self.q_posterior(x_start = x_start, x_t = x, t = t)
-        return model_mean, posterior_variance, posterior_log_variance
+        return model_mean, posterior_variance, posterior_log_variance, x_start
 
     @torch.no_grad()
-    def p_sample(self, x, t: int, clip_denoised = True):
+    def p_sample(self, x, t: int, x_self_cond = None, clip_denoised = True):
         b, *_, device = *x.shape, x.device
         batched_times = torch.full((x.shape[0],), t, device = x.device, dtype = torch.long)
-        model_mean, _, model_log_variance = self.p_mean_variance(x = x, t = batched_times, clip_denoised = clip_denoised)
+        model_mean, _, model_log_variance, x_start = self.p_mean_variance(x = x, t = batched_times, x_self_cond = x_self_cond, clip_denoised = clip_denoised)
         noise = torch.randn_like(x) if t > 0 else 0. # no noise if t == 0
-        return model_mean + (0.5 * model_log_variance).exp() * noise
+        pred_img = model_mean + (0.5 * model_log_variance).exp() * noise
+        return pred_img, x_start
 
     @torch.no_grad()
     def p_sample_loop(self, shape):
@@ -531,8 +582,11 @@ class GaussianDiffusion(nn.Module):
 
         img = torch.randn(shape, device=device)
 
-        for t in tqdm(reversed(range(0, self.num_timesteps)), desc = 'sampling loop time step'):
+        x_start = None
-            img = self.p_sample(img, t)
+
+        for t in tqdm(reversed(range(0, self.num_timesteps)), desc = 'sampling loop time step', total = self.num_timesteps):
+            self_cond = x_start if self.self_condition else None
+            img, x_start = self.p_sample(img, t, self_cond)
 
         img = unnormalize_to_zero_to_one(img)
         return img
@@ -541,27 +595,30 @@ class GaussianDiffusion(nn.Module):
     def ddim_sample(self, shape, clip_denoised = True):
         batch, device, total_timesteps, sampling_timesteps, eta, objective = shape[0], self.betas.device, self.num_timesteps, self.sampling_timesteps, self.ddim_sampling_eta, self.objective
 
-        times = torch.linspace(0., total_timesteps, steps = sampling_timesteps + 2)[:-1]
+        times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1)   # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps
         times = list(reversed(times.int().tolist()))
-        time_pairs = list(zip(times[:-1], times[1:]))
+        time_pairs = list(zip(times[:-1], times[1:])) # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)]
 
         img = torch.randn(shape, device = device)
 
+        x_start = None
+
         for time, time_next in tqdm(time_pairs, desc = 'sampling loop time step'):
-            alpha = self.alphas_cumprod_prev[time]
+            time_cond = torch.full((batch,), time, device=device, dtype=torch.long)
-            alpha_next = self.alphas_cumprod_prev[time_next]
+            self_cond = x_start if self.self_condition else None
+            pred_noise, x_start, *_ = self.model_predictions(img, time_cond, self_cond, clip_x_start = clip_denoised)
 
-            time_cond = torch.full((batch,), time, device = device, dtype = torch.long)
+            if time_next < 0:
+                img = x_start
+                continue
 
-            pred_noise, x_start, *_ = self.model_predictions(img, time_cond)
+            alpha = self.alphas_cumprod[time]
-
+            alpha_next = self.alphas_cumprod[time_next]
-            if clip_denoised:
-                x_start.clamp_(-1., 1.)
 
             sigma = eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt()
-            c = ((1 - alpha_next) - sigma ** 2).sqrt()
+            c = (1 - alpha_next - sigma ** 2).sqrt()
 
-            noise = torch.randn_like(img) if time_next > 0 else 0.
+            noise = torch.randn_like(img)
 
             img = x_start * alpha_next.sqrt() + \
                   c * pred_noise + \
@@ -583,11 +640,11 @@ class GaussianDiffusion(nn.Module):
 
         assert x1.shape == x2.shape
 
-        t_batched = torch.stack([torch.tensor(t, device=device)] * b)
+        t_batched = torch.stack([torch.tensor(t, device = device)] * b)
-        xt1, xt2 = map(lambda x: self.q_sample(x, t=t_batched), (x1, x2))
+        xt1, xt2 = map(lambda x: self.q_sample(x, t = t_batched), (x1, x2))
 
         img = (1 - lam) * xt1 + lam * xt2
-        for i in tqdm(reversed(range(0, t)), desc='interpolation sample time step', total=t):
+        for i in tqdm(reversed(range(0, t)), desc = 'interpolation sample time step', total = t):
             img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))
 
         return img
@@ -613,13 +670,31 @@ class GaussianDiffusion(nn.Module):
         b, c, h, w = x_start.shape
         noise = default(noise, lambda: torch.randn_like(x_start))
 
+        # noise sample
+
         x = self.q_sample(x_start = x_start, t = t, noise = noise)
-        model_out = self.model(x, t)
+
+        # if doing self-conditioning, 50% of the time, predict x_start from current set of times
+        # and condition with unet with that
+        # this technique will slow down training by 25%, but seems to lower FID significantly
+
+        x_self_cond = None
+        if self.self_condition and random() < 0.5:
+            with torch.no_grad():
+                x_self_cond = self.model_predictions(x, t).pred_x_start
+                x_self_cond.detach_()
+
+        # predict and take gradient step
+
+        model_out = self.model(x, t, x_self_cond)
 
         if self.objective == 'pred_noise':
             target = noise
         elif self.objective == 'pred_x0':
             target = x_start
+        elif self.objective == 'pred_v':
+            v = self.predict_v(x_start, t, noise)
+            target = v
         else:
             raise ValueError(f'unknown objective {self.objective}')
 
@@ -653,7 +728,7 @@ class Dataset(Dataset):
         self.image_size = image_size
         self.paths = [p for ext in exts for p in Path(f'{folder}').glob(f'**/*.{ext}')]
 
-        maybe_convert_fn = partial(convert_image_to, convert_image_to) if exists(convert_image_to) else nn.Identity()
+        maybe_convert_fn = partial(convert_image_to_fn, convert_image_to) if exists(convert_image_to) else nn.Identity()
 
         self.transform = T.Compose([
             T.Lambda(maybe_convert_fn),
@@ -759,7 +834,10 @@ class Trainer(object):
         torch.save(data, str(self.results_folder / f'model-{milestone}.pt'))
 
     def load(self, milestone):
-        data = torch.load(str(self.results_folder / f'model-{milestone}.pt'))
+        accelerator = self.accelerator
+        device = accelerator.device
+
+        data = torch.load(str(self.results_folder / f'model-{milestone}.pt'), map_location=device)
 
         model = self.accelerator.unwrap_model(self.model)
         model.load_state_dict(data['model'])
@@ -791,6 +869,7 @@ class Trainer(object):
 
                     self.accelerator.backward(loss)
 
+                accelerator.clip_grad_norm_(self.model.parameters(), 1.0)
                 pbar.set_description(f'loss: {total_loss:.4f}')
 
                 accelerator.wait_for_everyone()
@@ -800,6 +879,7 @@ class Trainer(object):
 
                 accelerator.wait_for_everyone()
 
+                self.step += 1
                 if accelerator.is_main_process:
                     self.ema.to(device)
                     self.ema.update()
@@ -816,7 +896,6 @@ class Trainer(object):
                         utils.save_image(all_images, str(self.results_folder / f'sample-{milestone}.png'), nrow = int(math.sqrt(self.num_samples)))
                         self.save(milestone)
 
-                self.step += 1
                 pbar.update(1)
 
         accelerator.print('training complete')

denoising_diffusion_pytorch/denoising_diffusion_pytorch_1d.py

@@ -0,0 +1,695 @@
+import math
+from random import random
+from functools import partial
+from collections import namedtuple
+
+import torch
+from torch import nn, einsum
+import torch.nn.functional as F
+
+from einops import rearrange, reduce
+from einops.layers.torch import Rearrange
+
+from tqdm.auto import tqdm
+
+# constants
+
+ModelPrediction =  namedtuple('ModelPrediction', ['pred_noise', 'pred_x_start'])
+
+# helpers functions
+
+def exists(x):
+    return x is not None
+
+def default(val, d):
+    if exists(val):
+        return val
+    return d() if callable(d) else d
+
+def identity(t, *args, **kwargs):
+    return t
+
+def cycle(dl):
+    while True:
+        for data in dl:
+            yield data
+
+def has_int_squareroot(num):
+    return (math.sqrt(num) ** 2) == num
+
+def num_to_groups(num, divisor):
+    groups = num // divisor
+    remainder = num % divisor
+    arr = [divisor] * groups
+    if remainder > 0:
+        arr.append(remainder)
+    return arr
+
+def convert_image_to_fn(img_type, image):
+    if image.mode != img_type:
+        return image.convert(img_type)
+    return image
+
+# normalization functions
+
+def normalize_to_neg_one_to_one(img):
+    return img * 2 - 1
+
+def unnormalize_to_zero_to_one(t):
+    return (t + 1) * 0.5
+
+# small helper modules
+
+class Residual(nn.Module):
+    def __init__(self, fn):
+        super().__init__()
+        self.fn = fn
+
+    def forward(self, x, *args, **kwargs):
+        return self.fn(x, *args, **kwargs) + x
+
+def Upsample(dim, dim_out = None):
+    return nn.Sequential(
+        nn.Upsample(scale_factor = 2, mode = 'nearest'),
+        nn.Conv1d(dim, default(dim_out, dim), 3, padding = 1)
+    )
+
+def Downsample(dim, dim_out = None):
+    return nn.Conv1d(dim, default(dim_out, dim), 4, 2, 1)
+
+class WeightStandardizedConv2d(nn.Conv1d):
+    """
+    https://arxiv.org/abs/1903.10520
+    weight standardization purportedly works synergistically with group normalization
+    """
+    def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
+
+        weight = self.weight
+        mean = reduce(weight, 'o ... -> o 1 1', 'mean')
+        var = reduce(weight, 'o ... -> o 1 1', partial(torch.var, unbiased = False))
+        normalized_weight = (weight - mean) * (var + eps).rsqrt()
+
+        return F.conv1d(x, normalized_weight, self.bias, self.stride, self.padding, self.dilation, self.groups)
+
+class LayerNorm(nn.Module):
+    def __init__(self, dim):
+        super().__init__()
+        self.g = nn.Parameter(torch.ones(1, dim, 1))
+
+    def forward(self, x):
+        eps = 1e-5 if x.dtype == torch.float32 else 1e-3
+        var = torch.var(x, dim = 1, unbiased = False, keepdim = True)
+        mean = torch.mean(x, dim = 1, keepdim = True)
+        return (x - mean) * (var + eps).rsqrt() * self.g
+
+class PreNorm(nn.Module):
+    def __init__(self, dim, fn):
+        super().__init__()
+        self.fn = fn
+        self.norm = LayerNorm(dim)
+
+    def forward(self, x):
+        x = self.norm(x)
+        return self.fn(x)
+
+# sinusoidal positional embeds
+
+class SinusoidalPosEmb(nn.Module):
+    def __init__(self, dim):
+        super().__init__()
+        self.dim = dim
+
+    def forward(self, x):
+        device = x.device
+        half_dim = self.dim // 2
+        emb = math.log(10000) / (half_dim - 1)
+        emb = torch.exp(torch.arange(half_dim, device=device) * -emb)
+        emb = x[:, None] * emb[None, :]
+        emb = torch.cat((emb.sin(), emb.cos()), dim=-1)
+        return emb
+
+class RandomOrLearnedSinusoidalPosEmb(nn.Module):
+    """ following @crowsonkb 's lead with random (learned optional) sinusoidal pos emb """
+    """ https://github.com/crowsonkb/v-diffusion-jax/blob/master/diffusion/models/danbooru_128.py#L8 """
+
+    def __init__(self, dim, is_random = False):
+        super().__init__()
+        assert (dim % 2) == 0
+        half_dim = dim // 2
+        self.weights = nn.Parameter(torch.randn(half_dim), requires_grad = not is_random)
+
+    def forward(self, x):
+        x = rearrange(x, 'b -> b 1')
+        freqs = x * rearrange(self.weights, 'd -> 1 d') * 2 * math.pi
+        fouriered = torch.cat((freqs.sin(), freqs.cos()), dim = -1)
+        fouriered = torch.cat((x, fouriered), dim = -1)
+        return fouriered
+
+# building block modules
+
+class Block(nn.Module):
+    def __init__(self, dim, dim_out, groups = 8):
+        super().__init__()
+        self.proj = WeightStandardizedConv2d(dim, dim_out, 3, padding = 1)
+        self.norm = nn.GroupNorm(groups, dim_out)
+        self.act = nn.SiLU()
+
+    def forward(self, x, scale_shift = None):
+        x = self.proj(x)
+        x = self.norm(x)
+
+        if exists(scale_shift):
+            scale, shift = scale_shift
+            x = x * (scale + 1) + shift
+
+        x = self.act(x)
+        return x
+
+class ResnetBlock(nn.Module):
+    def __init__(self, dim, dim_out, *, time_emb_dim = None, groups = 8):
+        super().__init__()
+        self.mlp = nn.Sequential(
+            nn.SiLU(),
+            nn.Linear(time_emb_dim, dim_out * 2)
+        ) if exists(time_emb_dim) else None
+
+        self.block1 = Block(dim, dim_out, groups = groups)
+        self.block2 = Block(dim_out, dim_out, groups = groups)
+        self.res_conv = nn.Conv1d(dim, dim_out, 1) if dim != dim_out else nn.Identity()
+
+    def forward(self, x, time_emb = None):
+
+        scale_shift = None
+        if exists(self.mlp) and exists(time_emb):
+            time_emb = self.mlp(time_emb)
+            time_emb = rearrange(time_emb, 'b c -> b c 1')
+            scale_shift = time_emb.chunk(2, dim = 1)
+
+        h = self.block1(x, scale_shift = scale_shift)
+
+        h = self.block2(h)
+
+        return h + self.res_conv(x)
+
+class LinearAttention(nn.Module):
+    def __init__(self, dim, heads = 4, dim_head = 32):
+        super().__init__()
+        self.scale = dim_head ** -0.5
+        self.heads = heads
+        hidden_dim = dim_head * heads
+        self.to_qkv = nn.Conv1d(dim, hidden_dim * 3, 1, bias = False)
+
+        self.to_out = nn.Sequential(
+            nn.Conv1d(hidden_dim, dim, 1),
+            LayerNorm(dim)
+        )
+
+    def forward(self, x):
+        b, c, n = x.shape
+        qkv = self.to_qkv(x).chunk(3, dim = 1)
+        q, k, v = map(lambda t: rearrange(t, 'b (h c) n -> b h c n', h = self.heads), qkv)
+
+        q = q.softmax(dim = -2)
+        k = k.softmax(dim = -1)
+
+        q = q * self.scale        
+
+        context = torch.einsum('b h d n, b h e n -> b h d e', k, v)
+
+        out = torch.einsum('b h d e, b h d n -> b h e n', context, q)
+        out = rearrange(out, 'b h c n -> b (h c) n', h = self.heads)
+        return self.to_out(out)
+
+class Attention(nn.Module):
+    def __init__(self, dim, heads = 4, dim_head = 32):
+        super().__init__()
+        self.scale = dim_head ** -0.5
+        self.heads = heads
+        hidden_dim = dim_head * heads
+
+        self.to_qkv = nn.Conv1d(dim, hidden_dim * 3, 1, bias = False)
+        self.to_out = nn.Conv1d(hidden_dim, dim, 1)
+
+    def forward(self, x):
+        b, c, n = x.shape
+        qkv = self.to_qkv(x).chunk(3, dim = 1)
+        q, k, v = map(lambda t: rearrange(t, 'b (h c) n -> b h c n', h = self.heads), qkv)
+
+        q = q * self.scale
+
+        sim = einsum('b h d i, b h d j -> b h i j', q, k)
+        attn = sim.softmax(dim = -1)
+        out = einsum('b h i j, b h d j -> b h i d', attn, v)
+
+        out = rearrange(out, 'b h n d -> b (h d) n')
+        return self.to_out(out)
+
+# model
+
+class Unet1D(nn.Module):
+    def __init__(
+        self,
+        dim,
+        init_dim = None,
+        out_dim = None,
+        dim_mults=(1, 2, 4, 8),
+        channels = 3,
+        self_condition = False,
+        resnet_block_groups = 8,
+        learned_variance = False,
+        learned_sinusoidal_cond = False,
+        random_fourier_features = False,
+        learned_sinusoidal_dim = 16
+    ):
+        super().__init__()
+
+        # determine dimensions
+
+        self.channels = channels
+        self.self_condition = self_condition
+        input_channels = channels * (2 if self_condition else 1)
+
+        init_dim = default(init_dim, dim)
+        self.init_conv = nn.Conv1d(input_channels, init_dim, 7, padding = 3)
+
+        dims = [init_dim, *map(lambda m: dim * m, dim_mults)]
+        in_out = list(zip(dims[:-1], dims[1:]))
+
+        block_klass = partial(ResnetBlock, groups = resnet_block_groups)
+
+        # time embeddings
+
+        time_dim = dim * 4
+
+        self.random_or_learned_sinusoidal_cond = learned_sinusoidal_cond or random_fourier_features
+
+        if self.random_or_learned_sinusoidal_cond:
+            sinu_pos_emb = RandomOrLearnedSinusoidalPosEmb(learned_sinusoidal_dim, random_fourier_features)
+            fourier_dim = learned_sinusoidal_dim + 1
+        else:
+            sinu_pos_emb = SinusoidalPosEmb(dim)
+            fourier_dim = dim
+
+        self.time_mlp = nn.Sequential(
+            sinu_pos_emb,
+            nn.Linear(fourier_dim, time_dim),
+            nn.GELU(),
+            nn.Linear(time_dim, time_dim)
+        )
+
+        # layers
+
+        self.downs = nn.ModuleList([])
+        self.ups = nn.ModuleList([])
+        num_resolutions = len(in_out)
+
+        for ind, (dim_in, dim_out) in enumerate(in_out):
+            is_last = ind >= (num_resolutions - 1)
+
+            self.downs.append(nn.ModuleList([
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim),
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim),
+                Residual(PreNorm(dim_in, LinearAttention(dim_in))),
+                Downsample(dim_in, dim_out) if not is_last else nn.Conv1d(dim_in, dim_out, 3, padding = 1)
+            ]))
+
+        mid_dim = dims[-1]
+        self.mid_block1 = block_klass(mid_dim, mid_dim, time_emb_dim = time_dim)
+        self.mid_attn = Residual(PreNorm(mid_dim, Attention(mid_dim)))
+        self.mid_block2 = block_klass(mid_dim, mid_dim, time_emb_dim = time_dim)
+
+        for ind, (dim_in, dim_out) in enumerate(reversed(in_out)):
+            is_last = ind == (len(in_out) - 1)
+
+            self.ups.append(nn.ModuleList([
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim),
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim),
+                Residual(PreNorm(dim_out, LinearAttention(dim_out))),
+                Upsample(dim_out, dim_in) if not is_last else  nn.Conv1d(dim_out, dim_in, 3, padding = 1)
+            ]))
+
+        default_out_dim = channels * (1 if not learned_variance else 2)
+        self.out_dim = default(out_dim, default_out_dim)
+
+        self.final_res_block = block_klass(dim * 2, dim, time_emb_dim = time_dim)
+        self.final_conv = nn.Conv1d(dim, self.out_dim, 1)
+
+    def forward(self, x, time, x_self_cond = None):
+        if self.self_condition:
+            x_self_cond = default(x_self_cond, lambda: torch.zeros_like(x))
+            x = torch.cat((x_self_cond, x), dim = 1)
+
+        x = self.init_conv(x)
+        r = x.clone()
+
+        t = self.time_mlp(time)
+
+        h = []
+
+        for block1, block2, attn, downsample in self.downs:
+            x = block1(x, t)
+            h.append(x)
+
+            x = block2(x, t)
+            x = attn(x)
+            h.append(x)
+
+            x = downsample(x)
+
+        x = self.mid_block1(x, t)
+        x = self.mid_attn(x)
+        x = self.mid_block2(x, t)
+
+        for block1, block2, attn, upsample in self.ups:
+            x = torch.cat((x, h.pop()), dim = 1)
+            x = block1(x, t)
+
+            x = torch.cat((x, h.pop()), dim = 1)
+            x = block2(x, t)
+            x = attn(x)
+
+            x = upsample(x)
+
+        x = torch.cat((x, r), dim = 1)
+
+        x = self.final_res_block(x, t)
+        return self.final_conv(x)
+
+# gaussian diffusion trainer class
+
+def extract(a, t, x_shape):
+    b, *_ = t.shape
+    out = a.gather(-1, t)
+    return out.reshape(b, *((1,) * (len(x_shape) - 1)))
+
+def linear_beta_schedule(timesteps):
+    scale = 1000 / timesteps
+    beta_start = scale * 0.0001
+    beta_end = scale * 0.02
+    return torch.linspace(beta_start, beta_end, timesteps, dtype = torch.float64)
+
+def cosine_beta_schedule(timesteps, s = 0.008):
+    """
+    cosine schedule
+    as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
+    """
+    steps = timesteps + 1
+    x = torch.linspace(0, timesteps, steps, dtype = torch.float64)
+    alphas_cumprod = torch.cos(((x / timesteps) + s) / (1 + s) * math.pi * 0.5) ** 2
+    alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
+    betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
+    return torch.clip(betas, 0, 0.999)
+
+class GaussianDiffusion1D(nn.Module):
+    def __init__(
+        self,
+        model,
+        *,
+        seq_length,
+        timesteps = 1000,
+        sampling_timesteps = None,
+        loss_type = 'l1',
+        objective = 'pred_noise',
+        beta_schedule = 'cosine',
+        p2_loss_weight_gamma = 0.,
+        p2_loss_weight_k = 1,
+        ddim_sampling_eta = 1.
+    ):
+        super().__init__()
+        self.model = model
+        self.channels = self.model.channels
+        self.self_condition = self.model.self_condition
+
+        self.seq_length = seq_length
+
+        self.objective = objective
+
+        assert objective in {'pred_noise', 'pred_x0', 'pred_v'}, 'objective must be either pred_noise (predict noise) or pred_x0 (predict image start) or pred_v (predict v [v-parameterization as defined in appendix D of progressive distillation paper, used in imagen-video successfully])'
+
+        if beta_schedule == 'linear':
+            betas = linear_beta_schedule(timesteps)
+        elif beta_schedule == 'cosine':
+            betas = cosine_beta_schedule(timesteps)
+        else:
+            raise ValueError(f'unknown beta schedule {beta_schedule}')
+
+        alphas = 1. - betas
+        alphas_cumprod = torch.cumprod(alphas, dim=0)
+        alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value = 1.)
+
+        timesteps, = betas.shape
+        self.num_timesteps = int(timesteps)
+        self.loss_type = loss_type
+
+        # sampling related parameters
+
+        self.sampling_timesteps = default(sampling_timesteps, timesteps) # default num sampling timesteps to number of timesteps at training
+
+        assert self.sampling_timesteps <= timesteps
+        self.is_ddim_sampling = self.sampling_timesteps < timesteps
+        self.ddim_sampling_eta = ddim_sampling_eta
+
+        # helper function to register buffer from float64 to float32
+
+        register_buffer = lambda name, val: self.register_buffer(name, val.to(torch.float32))
+
+        register_buffer('betas', betas)
+        register_buffer('alphas_cumprod', alphas_cumprod)
+        register_buffer('alphas_cumprod_prev', alphas_cumprod_prev)
+
+        # calculations for diffusion q(x_t | x_{t-1}) and others
+
+        register_buffer('sqrt_alphas_cumprod', torch.sqrt(alphas_cumprod))
+        register_buffer('sqrt_one_minus_alphas_cumprod', torch.sqrt(1. - alphas_cumprod))
+        register_buffer('log_one_minus_alphas_cumprod', torch.log(1. - alphas_cumprod))
+        register_buffer('sqrt_recip_alphas_cumprod', torch.sqrt(1. / alphas_cumprod))
+        register_buffer('sqrt_recipm1_alphas_cumprod', torch.sqrt(1. / alphas_cumprod - 1))
+
+        # calculations for posterior q(x_{t-1} | x_t, x_0)
+
+        posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod)
+
+        # above: equal to 1. / (1. / (1. - alpha_cumprod_tm1) + alpha_t / beta_t)
+
+        register_buffer('posterior_variance', posterior_variance)
+
+        # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain
+
+        register_buffer('posterior_log_variance_clipped', torch.log(posterior_variance.clamp(min =1e-20)))
+        register_buffer('posterior_mean_coef1', betas * torch.sqrt(alphas_cumprod_prev) / (1. - alphas_cumprod))
+        register_buffer('posterior_mean_coef2', (1. - alphas_cumprod_prev) * torch.sqrt(alphas) / (1. - alphas_cumprod))
+
+        # calculate p2 reweighting
+
+        register_buffer('p2_loss_weight', (p2_loss_weight_k + alphas_cumprod / (1 - alphas_cumprod)) ** -p2_loss_weight_gamma)
+
+    def predict_start_from_noise(self, x_t, t, noise):
+        return (
+            extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * noise
+        )
+
+    def predict_noise_from_start(self, x_t, t, x0):
+        return (
+            (extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - x0) / \
+            extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
+        )
+
+    def predict_v(self, x_start, t, noise):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * noise -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * x_start
+        )
+
+    def predict_start_from_v(self, x_t, t, v):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_t.shape) * v
+        )
+
+    def q_posterior(self, x_start, x_t, t):
+        posterior_mean = (
+            extract(self.posterior_mean_coef1, t, x_t.shape) * x_start +
+            extract(self.posterior_mean_coef2, t, x_t.shape) * x_t
+        )
+        posterior_variance = extract(self.posterior_variance, t, x_t.shape)
+        posterior_log_variance_clipped = extract(self.posterior_log_variance_clipped, t, x_t.shape)
+        return posterior_mean, posterior_variance, posterior_log_variance_clipped
+
+    def model_predictions(self, x, t, x_self_cond = None, clip_x_start = False):
+        model_output = self.model(x, t, x_self_cond)
+        maybe_clip = partial(torch.clamp, min = -1., max = 1.) if clip_x_start else identity
+
+        if self.objective == 'pred_noise':
+            pred_noise = model_output
+            x_start = self.predict_start_from_noise(x, t, pred_noise)
+            x_start = maybe_clip(x_start)
+
+        elif self.objective == 'pred_x0':
+            x_start = model_output
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
+        elif self.objective == 'pred_v':
+            v = model_output
+            x_start = self.predict_start_from_v(x, t, v)
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
+        return ModelPrediction(pred_noise, x_start)
+
+    def p_mean_variance(self, x, t, x_self_cond = None, clip_denoised = True):
+        preds = self.model_predictions(x, t, x_self_cond)
+        x_start = preds.pred_x_start
+
+        if clip_denoised:
+            x_start.clamp_(-1., 1.)
+
+        model_mean, posterior_variance, posterior_log_variance = self.q_posterior(x_start = x_start, x_t = x, t = t)
+        return model_mean, posterior_variance, posterior_log_variance, x_start
+
+    @torch.no_grad()
+    def p_sample(self, x, t: int, x_self_cond = None, clip_denoised = True):
+        b, *_, device = *x.shape, x.device
+        batched_times = torch.full((x.shape[0],), t, device = x.device, dtype = torch.long)
+        model_mean, _, model_log_variance, x_start = self.p_mean_variance(x = x, t = batched_times, x_self_cond = x_self_cond, clip_denoised = clip_denoised)
+        noise = torch.randn_like(x) if t > 0 else 0. # no noise if t == 0
+        pred_img = model_mean + (0.5 * model_log_variance).exp() * noise
+        return pred_img, x_start
+
+    @torch.no_grad()
+    def p_sample_loop(self, shape):
+        batch, device = shape[0], self.betas.device
+
+        img = torch.randn(shape, device=device)
+
+        x_start = None
+
+        for t in tqdm(reversed(range(0, self.num_timesteps)), desc = 'sampling loop time step', total = self.num_timesteps):
+            self_cond = x_start if self.self_condition else None
+            img, x_start = self.p_sample(img, t, self_cond)
+
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def ddim_sample(self, shape, clip_denoised = True):
+        batch, device, total_timesteps, sampling_timesteps, eta, objective = shape[0], self.betas.device, self.num_timesteps, self.sampling_timesteps, self.ddim_sampling_eta, self.objective
+
+        times = torch.linspace(-1, total_timesteps - 1, steps=sampling_timesteps + 1)   # [-1, 0, 1, 2, ..., T-1] when sampling_timesteps == total_timesteps
+        times = list(reversed(times.int().tolist()))
+        time_pairs = list(zip(times[:-1], times[1:])) # [(T-1, T-2), (T-2, T-3), ..., (1, 0), (0, -1)]
+
+        img = torch.randn(shape, device = device)
+
+        x_start = None
+
+        for time, time_next in tqdm(time_pairs, desc = 'sampling loop time step'):
+            time_cond = torch.full((batch,), time, device=device, dtype=torch.long)
+            self_cond = x_start if self.self_condition else None
+            pred_noise, x_start, *_ = self.model_predictions(img, time_cond, self_cond, clip_x_start = clip_denoised)
+
+            if time_next < 0:
+                img = x_start
+                continue
+
+            alpha = self.alphas_cumprod[time]
+            alpha_next = self.alphas_cumprod[time_next]
+
+            sigma = eta * ((1 - alpha / alpha_next) * (1 - alpha_next) / (1 - alpha)).sqrt()
+            c = (1 - alpha_next - sigma ** 2).sqrt()
+
+            noise = torch.randn_like(img)
+
+            img = x_start * alpha_next.sqrt() + \
+                  c * pred_noise + \
+                  sigma * noise
+
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def sample(self, batch_size = 16):
+        seq_length, channels = self.seq_length, self.channels
+        sample_fn = self.p_sample_loop if not self.is_ddim_sampling else self.ddim_sample
+        return sample_fn((batch_size, channels, seq_length))
+
+    @torch.no_grad()
+    def interpolate(self, x1, x2, t = None, lam = 0.5):
+        b, *_, device = *x1.shape, x1.device
+        t = default(t, self.num_timesteps - 1)
+
+        assert x1.shape == x2.shape
+
+        t_batched = torch.stack([torch.tensor(t, device = device)] * b)
+        xt1, xt2 = map(lambda x: self.q_sample(x, t = t_batched), (x1, x2))
+
+        img = (1 - lam) * xt1 + lam * xt2
+        for i in tqdm(reversed(range(0, t)), desc = 'interpolation sample time step', total = t):
+            img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))
+
+        return img
+
+    def q_sample(self, x_start, t, noise=None):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start +
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise
+        )
+
+    @property
+    def loss_fn(self):
+        if self.loss_type == 'l1':
+            return F.l1_loss
+        elif self.loss_type == 'l2':
+            return F.mse_loss
+        else:
+            raise ValueError(f'invalid loss type {self.loss_type}')
+
+    def p_losses(self, x_start, t, noise = None):
+        b, c, n = x_start.shape
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        # noise sample
+
+        x = self.q_sample(x_start = x_start, t = t, noise = noise)
+
+        # if doing self-conditioning, 50% of the time, predict x_start from current set of times
+        # and condition with unet with that
+        # this technique will slow down training by 25%, but seems to lower FID significantly
+
+        x_self_cond = None
+        if self.self_condition and random() < 0.5:
+            with torch.no_grad():
+                x_self_cond = self.model_predictions(x, t).pred_x_start
+                x_self_cond.detach_()
+
+        # predict and take gradient step
+
+        model_out = self.model(x, t, x_self_cond)
+
+        if self.objective == 'pred_noise':
+            target = noise
+        elif self.objective == 'pred_x0':
+            target = x_start
+        elif self.objective == 'pred_v':
+            v = self.predict_v(x_start, t, noise)
+            target = v
+        else:
+            raise ValueError(f'unknown objective {self.objective}')
+
+        loss = self.loss_fn(model_out, target, reduction = 'none')
+        loss = reduce(loss, 'b ... -> b (...)', 'mean')
+
+        loss = loss * extract(self.p2_loss_weight, t, loss.shape)
+        return loss.mean()
+
+    def forward(self, img, *args, **kwargs):
+        b, c, n, device, seq_length, = *img.shape, img.device, self.seq_length
+        assert n == seq_length, f'seq length must be {seq_length}'
+        t = torch.randint(0, self.num_timesteps, (b,), device=device).long()
+
+        img = normalize_to_neg_one_to_one(img)
+        return self.p_losses(img, t, *args, **kwargs)

denoising_diffusion_pytorch/elucidated_diffusion.py

@@ -1,4 +1,5 @@
 from math import sqrt
+from random import random
 import torch
 from torch import nn, einsum
 import torch.nn.functional as F
@@ -51,7 +52,8 @@ class ElucidatedDiffusion(nn.Module):
         S_noise = 1.003,
     ):
         super().__init__()
-        assert net.learned_sinusoidal_cond
+        assert net.random_or_learned_sinusoidal_cond
+        self.self_condition = net.self_condition
 
         self.net = net
 
@@ -99,7 +101,7 @@ class ElucidatedDiffusion(nn.Module):
     # preconditioned network output
     # equation (7) in the paper
 
-    def preconditioned_network_forward(self, noised_images, sigma, clamp = False):
+    def preconditioned_network_forward(self, noised_images, sigma, self_cond = None, clamp = False):
         batch, device = noised_images.shape[0], noised_images.device
 
         if isinstance(sigma, float):
@@ -109,7 +111,8 @@ class ElucidatedDiffusion(nn.Module):
 
         net_out = self.net(
             self.c_in(padded_sigma) * noised_images,
-            self.c_noise(sigma)
+            self.c_noise(sigma),
+            self_cond
         )
 
         out = self.c_skip(padded_sigma) * noised_images +  self.c_out(padded_sigma) * net_out
@@ -160,6 +163,10 @@ class ElucidatedDiffusion(nn.Module):
 
         images = init_sigma * torch.randn(shape, device = self.device)
 
+        # for self conditioning
+
+        x_start = None
+
         # gradually denoise
 
         for sigma, sigma_next, gamma in tqdm(sigmas_and_gammas, desc = 'sampling time step'):
@@ -170,7 +177,9 @@ class ElucidatedDiffusion(nn.Module):
             sigma_hat = sigma + gamma * sigma
             images_hat = images + sqrt(sigma_hat ** 2 - sigma ** 2) * eps
 
-            model_output = self.preconditioned_network_forward(images_hat, sigma_hat, clamp = clamp)
+            self_cond = x_start if self.self_condition else None
+
+            model_output = self.preconditioned_network_forward(images_hat, sigma_hat, self_cond, clamp = clamp)
             denoised_over_sigma = (images_hat - model_output) / sigma_hat
 
             images_next = images_hat + (sigma_next - sigma_hat) * denoised_over_sigma
@@ -178,11 +187,14 @@ class ElucidatedDiffusion(nn.Module):
             # second order correction, if not the last timestep
 
             if sigma_next != 0:
-                model_output_next = self.preconditioned_network_forward(images_next, sigma_next, clamp = clamp)
+                self_cond = model_output if self.self_condition else None
+
+                model_output_next = self.preconditioned_network_forward(images_next, sigma_next, self_cond, clamp = clamp)
                 denoised_prime_over_sigma = (images_next - model_output_next) / sigma_next
                 images_next = images_hat + 0.5 * (sigma_next - sigma_hat) * (denoised_over_sigma + denoised_prime_over_sigma)
 
             images = images_next
+            x_start = model_output
 
         images = images.clamp(-1., 1.)
         return unnormalize_to_zero_to_one(images)
@@ -210,7 +222,15 @@ class ElucidatedDiffusion(nn.Module):
 
         noised_images = images + padded_sigmas * noise  # alphas are 1. in the paper
 
-        denoised = self.preconditioned_network_forward(noised_images, sigmas)
+        self_cond = None
+
+        if self.self_condition and random() < 0.5:
+            # from hinton's group's bit diffusion paper
+            with torch.no_grad():
+                self_cond = self.preconditioned_network_forward(noised_images, sigmas)
+                self_cond.detach_()
+
+        denoised = self.preconditioned_network_forward(noised_images, sigmas, self_cond)
 
         losses = F.mse_loss(denoised, images, reduction = 'none')
         losses = reduce(losses, 'b ... -> b', 'mean')

denoising_diffusion_pytorch/learned_gaussian_diffusion.py

@@ -77,6 +77,8 @@ class LearnedGaussianDiffusion(GaussianDiffusion):
     ):
         super().__init__(model, *args, **kwargs)
         assert model.out_dim == (model.channels * 2), 'dimension out of unet must be twice the number of channels for learned variance - you can also set the `learned_variance` keyword argument on the Unet to be `True`'
+        assert not model.self_condition, 'not supported yet'
+
         self.vb_loss_weight = vb_loss_weight
 
     def model_predictions(self, x, t):

denoising_diffusion_pytorch/v_param_continuous_time_gaussian_diffusion.py

@@ -0,0 +1,184 @@
+import math
+import torch
+from torch import sqrt
+from torch import nn, einsum
+import torch.nn.functional as F
+from torch.special import expm1
+
+from tqdm import tqdm
+from einops import rearrange, repeat, reduce
+from einops.layers.torch import Rearrange
+
+# helpers
+
+def exists(val):
+    return val is not None
+
+def default(val, d):
+    if exists(val):
+        return val
+    return d() if callable(d) else d
+
+# normalization functions
+
+def normalize_to_neg_one_to_one(img):
+    return img * 2 - 1
+
+def unnormalize_to_zero_to_one(t):
+    return (t + 1) * 0.5
+
+# diffusion helpers
+
+def right_pad_dims_to(x, t):
+    padding_dims = x.ndim - t.ndim
+    if padding_dims <= 0:
+        return t
+    return t.view(*t.shape, *((1,) * padding_dims))
+
+# continuous schedules
+# log(snr) that approximates the original linear schedule
+
+def log(t, eps = 1e-20):
+    return torch.log(t.clamp(min = eps))
+
+def alpha_cosine_log_snr(t, s = 0.008):
+    return -log((torch.cos((t + s) / (1 + s) * math.pi * 0.5) ** -2) - 1, eps = 1e-5)
+
+class VParamContinuousTimeGaussianDiffusion(nn.Module):
+    """
+    a new type of parameterization in v-space proposed in https://arxiv.org/abs/2202.00512 that
+    (1) allows for improved distillation over noise prediction objective and
+    (2) noted in imagen-video to improve upsampling unets by removing the color shifting artifacts
+    """
+
+    def __init__(
+        self,
+        model,
+        *,
+        image_size,
+        channels = 3,
+        num_sample_steps = 500,
+        clip_sample_denoised = True,
+    ):
+        super().__init__()
+        assert model.random_or_learned_sinusoidal_cond
+        assert not model.self_condition, 'not supported yet'
+
+        self.model = model
+
+        # image dimensions
+
+        self.channels = channels
+        self.image_size = image_size
+
+        # continuous noise schedule related stuff
+
+        self.log_snr = alpha_cosine_log_snr
+
+        # sampling
+
+        self.num_sample_steps = num_sample_steps
+        self.clip_sample_denoised = clip_sample_denoised        
+
+    @property
+    def device(self):
+        return next(self.model.parameters()).device
+
+    def p_mean_variance(self, x, time, time_next):
+        # reviewer found an error in the equation in the paper (missing sigma)
+        # following - https://openreview.net/forum?id=2LdBqxc1Yv&noteId=rIQgH0zKsRt
+
+        log_snr = self.log_snr(time)
+        log_snr_next = self.log_snr(time_next)
+        c = -expm1(log_snr - log_snr_next)
+
+        squared_alpha, squared_alpha_next = log_snr.sigmoid(), log_snr_next.sigmoid()
+        squared_sigma, squared_sigma_next = (-log_snr).sigmoid(), (-log_snr_next).sigmoid()
+
+        alpha, sigma, alpha_next = map(sqrt, (squared_alpha, squared_sigma, squared_alpha_next))
+
+        batch_log_snr = repeat(log_snr, ' -> b', b = x.shape[0])
+
+        pred_v = self.model(x, batch_log_snr)
+
+        # shown in Appendix D in the paper
+        x_start = alpha * x - sigma * pred_v
+
+        if self.clip_sample_denoised:
+            x_start.clamp_(-1., 1.)
+
+        model_mean = alpha_next * (x * (1 - c) / alpha + c * x_start)
+
+        posterior_variance = squared_sigma_next * c
+
+        return model_mean, posterior_variance
+
+    # sampling related functions
+
+    @torch.no_grad()
+    def p_sample(self, x, time, time_next):
+        batch, *_, device = *x.shape, x.device
+
+        model_mean, model_variance = self.p_mean_variance(x = x, time = time, time_next = time_next)
+
+        if time_next == 0:
+            return model_mean
+
+        noise = torch.randn_like(x)
+        return model_mean + sqrt(model_variance) * noise
+
+    @torch.no_grad()
+    def p_sample_loop(self, shape):
+        batch = shape[0]
+
+        img = torch.randn(shape, device = self.device)
+        steps = torch.linspace(1., 0., self.num_sample_steps + 1, device = self.device)
+
+        for i in tqdm(range(self.num_sample_steps), desc = 'sampling loop time step', total = self.num_sample_steps):
+            times = steps[i]
+            times_next = steps[i + 1]
+            img = self.p_sample(img, times, times_next)
+
+        img.clamp_(-1., 1.)
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def sample(self, batch_size = 16):
+        return self.p_sample_loop((batch_size, self.channels, self.image_size, self.image_size))
+
+    # training related functions - noise prediction
+
+    def q_sample(self, x_start, times, noise = None):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        log_snr = self.log_snr(times)
+
+        log_snr_padded = right_pad_dims_to(x_start, log_snr)
+        alpha, sigma = sqrt(log_snr_padded.sigmoid()), sqrt((-log_snr_padded).sigmoid())
+        x_noised =  x_start * alpha + noise * sigma
+
+        return x_noised, log_snr, alpha, sigma
+
+    def random_times(self, batch_size):
+        return torch.zeros((batch_size,), device = self.device).float().uniform_(0, 1)
+
+    def p_losses(self, x_start, times, noise = None):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        x, log_snr, alpha, sigma = self.q_sample(x_start = x_start, times = times, noise = noise)
+
+        # described in section 4 as the prediction objective, with derivation in Appendix D
+        v = alpha * noise - sigma * x_start
+
+        model_out = self.model(x, log_snr)
+
+        return F.mse_loss(model_out, v)
+
+    def forward(self, img, *args, **kwargs):
+        b, c, h, w, device, img_size, = *img.shape, img.device, self.image_size
+        assert h == img_size and w == img_size, f'height and width of image must be {img_size}'
+
+        times = self.random_times(b)
+        img = normalize_to_neg_one_to_one(img)
+        return self.p_losses(img, times, *args, **kwargs)

denoising_diffusion_pytorch/weighted_objective_gaussian_diffusion.py

@@ -31,6 +31,7 @@ class WeightedObjectiveGaussianDiffusion(GaussianDiffusion):
         super().__init__(model, *args, **kwargs)
         channels = model.channels
         assert model.out_dim == (channels * 2 + 2), 'dimension out (out_dim) of unet must be twice the number of channels + 2 (for the softmax weighted sum) - for channels of 3, this should be (3 * 2) + 2 = 8'
+        assert not model.self_condition, 'not supported yet'
         assert not self.is_ddim_sampling, 'ddim sampling cannot be used'
 
         self.split_dims = (channels, channels, 2)

setup.py

@@ -3,7 +3,7 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.26.4',
+  version = '0.32.0',
   license='MIT',
   description = 'Denoising Diffusion Probabilistic Models - Pytorch',
   author = 'Phil Wang',
@@ -30,4 +30,4 @@ setup(
     'License :: OSI Approved :: MIT License',
     'Programming Language :: Python :: 3.6',
   ],
-)
+)