help researchers in need of 1d ddpm, ex. https://github.com/lucidrains/denoising-diffusion-pytorch/issues/116

Added gradient clipping.

README.md

@@ -1,4 +1,4 @@
-<img src="./denoising-diffusion.png" width="500px"></img>
+<img src="./images/denoising-diffusion.png" width="500px"></img>
 
 ## Denoising Diffusion Probabilistic Model, in Pytorch
 
@@ -8,9 +8,13 @@ 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>
 
-<img src="./sample.png" width="500px"><img>
+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)
 
@@ -60,15 +64,16 @@ model = Unet(
 diffusion = GaussianDiffusion(
     model,
     image_size = 128,
-    timesteps = 1000,   # number of steps
+    timesteps = 1000,           # number of steps
-    loss_type = 'l1'    # L1 or L2
+    sampling_timesteps = 250,   # number of sampling timesteps (using ddim for faster inference [see citation for ddim paper])
+    loss_type = 'l1'            # L1 or L2
 ).cuda()
 
 trainer = Trainer(
     diffusion,
     'path/to/your/images',
     train_batch_size = 32,
-    train_lr = 1e-4,
+    train_lr = 8e-5,
     train_num_steps = 700000,         # total training steps
     gradient_accumulate_every = 2,    # gradient accumulation steps
     ema_decay = 0.995,                # exponential moving average decay
@@ -80,6 +85,53 @@ trainer.train()
 
 Samples and model checkpoints will be logged to `./results` periodically
 
+## Multi-GPU Training
+
+The `Trainer` class is now equipped with <a href="https://huggingface.co/docs/accelerate/accelerator">🤗 Accelerator</a>. You can easily do multi-gpu training in two steps using their `accelerate` CLI
+
+At the project root directory, where the training script is, run
+
+```python
+$ accelerate config
+```
+
+Then, in the same directory
+
+```python
+$ accelerate launch train.py
+```
+
+## Miscellaenous
+
+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.randn(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
@@ -133,3 +185,54 @@ Samples and model checkpoints will be logged to `./results` periodically
     volume  = {abs/2204.00227}
 }
 ```
+
+```bibtex
+@article{Karras2022ElucidatingTD,
+    title   = {Elucidating the Design Space of Diffusion-Based Generative Models},
+    author  = {Tero Karras and Miika Aittala and Timo Aila and Samuli Laine},
+    journal = {ArXiv},
+    year    = {2022},
+    volume  = {abs/2206.00364}
+}
+```
+
+```bibtex
+@article{Song2021DenoisingDI,
+    title   = {Denoising Diffusion Implicit Models},
+    author  = {Jiaming Song and Chenlin Meng and Stefano Ermon},
+    journal = {ArXiv},
+    year    = {2021},
+    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}
+}
+```

denoising_diffusion_pytorch/__init__.py

@@ -3,3 +3,8 @@ from denoising_diffusion_pytorch.denoising_diffusion_pytorch import GaussianDiff
 from denoising_diffusion_pytorch.learned_gaussian_diffusion import LearnedGaussianDiffusion
 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/continuous_time_gaussian_diffusion.py

@@ -1,3 +1,4 @@
+import math
 import torch
 from torch import sqrt
 from torch import nn, einsum
@@ -66,7 +67,7 @@ def beta_linear_log_snr(t):
     return -log(expm1(1e-4 + 10 * (t ** 2)))
 
 def alpha_cosine_log_snr(t, s = 0.008):
-    return -log((torch.cos((t + s) / (1 + s) * torch.pi * 0.5) ** -2) - 1, eps = 1e-5)
+    return -log((torch.cos((t + s) / (1 + s) * math.pi * 0.5) ** -2) - 1, eps = 1e-5)
 
 class learned_noise_schedule(nn.Module):
     """ described in section H and then I.2 of the supplementary material for variational ddpm paper """
@@ -111,7 +112,7 @@ class learned_noise_schedule(nn.Module):
 class ContinuousTimeGaussianDiffusion(nn.Module):
     def __init__(
         self,
-        denoise_fn,
+        model,
         *,
         image_size,
         channels = 3,
@@ -125,9 +126,10 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         p2_loss_weight_k = 1
     ):
         super().__init__()
-        assert not denoise_fn.sinusoidal_cond_mlp
+        assert model.random_or_learned_sinusoidal_cond
+        assert not model.self_condition, 'not supported yet'
 
-        self.denoise_fn = denoise_fn
+        self.model = model
 
         # image dimensions
 
@@ -169,7 +171,7 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
 
     @property
     def device(self):
-        return next(self.denoise_fn.parameters()).device
+        return next(self.model.parameters()).device
 
     @property
     def loss_fn(self):
@@ -194,7 +196,7 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         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_noise = self.denoise_fn(x, batch_log_snr)
+        pred_noise = self.model(x, batch_log_snr)
 
         if self.clip_sample_denoised:
             x_start = (x - sigma * pred_noise) / alpha
@@ -265,7 +267,7 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         noise = default(noise, lambda: torch.randn_like(x_start))
 
         x, log_snr = self.q_sample(x_start = x_start, times = times, noise = noise)
-        model_out = self.denoise_fn(x, log_snr)
+        model_out = self.model(x, log_snr)
 
         losses = self.loss_fn(model_out, noise, reduction = 'none')
         losses = reduce(losses, 'b ... -> b', 'mean')

denoising_diffusion_pytorch/denoising_diffusion_pytorch.py

@@ -1,24 +1,32 @@
 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 torch.utils.data import Dataset, DataLoader
-from functools import partial
 
-from torch.utils import data
-from multiprocessing import cpu_count
-from torch.cuda.amp import autocast, GradScaler
-
-from pathlib import Path
 from torch.optim import Adam
-from torchvision import transforms, utils
+from torchvision import transforms as T, utils
-from PIL import Image
 
-from tqdm import tqdm
 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
+
+from accelerate import Accelerator
+
+# constants
+
+ModelPrediction =  namedtuple('ModelPrediction', ['pred_noise', 'pred_x_start'])
+
 # helpers functions
 
 def exists(x):
@@ -27,13 +35,19 @@ 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:
         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
@@ -42,6 +56,13 @@ def num_to_groups(num, divisor):
         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
 
@@ -50,21 +71,6 @@ def unnormalize_to_zero_to_one(t):
 
 # small helper modules
 
-class EMA():
-    def __init__(self, beta):
-        super().__init__()
-        self.beta = beta
-
-    def update_model_average(self, ma_model, current_model):
-        for current_params, ma_params in zip(current_model.parameters(), ma_model.parameters()):
-            old_weight, up_weight = ma_params.data, current_params.data
-            ma_params.data = self.update_average(old_weight, up_weight)
-
-    def update_average(self, old, new):
-        if old is None:
-            return new
-        return old * self.beta + (1 - self.beta) * new
-
 class Residual(nn.Module):
     def __init__(self, fn):
         super().__init__()
@@ -73,6 +79,53 @@ class Residual(nn.Module):
     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__()
@@ -87,40 +140,29 @@ class SinusoidalPosEmb(nn.Module):
         emb = torch.cat((emb.sin(), emb.cos()), dim=-1)
         return emb
 
-def Upsample(dim):
+class RandomOrLearnedSinusoidalPosEmb(nn.Module):
-    return nn.ConvTranspose2d(dim, dim, 4, 2, 1)
+    """ 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 Downsample(dim):
+    def __init__(self, dim, is_random = False):
-    return nn.Conv2d(dim, dim, 4, 2, 1)
-
-class LayerNorm(nn.Module):
-    def __init__(self, dim, eps = 1e-5):
         super().__init__()
-        self.eps = eps
+        assert (dim % 2) == 0
-        self.g = nn.Parameter(torch.ones(1, dim, 1, 1))
+        half_dim = dim // 2
-        self.b = nn.Parameter(torch.zeros(1, dim, 1, 1))
+        self.weights = nn.Parameter(torch.randn(half_dim), requires_grad = not is_random)
 
     def forward(self, x):
-        var = torch.var(x, dim = 1, unbiased = False, keepdim = True)
+        x = rearrange(x, 'b -> b 1')
-        mean = torch.mean(x, dim = 1, keepdim = True)
+        freqs = x * rearrange(self.weights, 'd -> 1 d') * 2 * math.pi
-        return (x - mean) / (var + self.eps).sqrt() * self.g + self.b
+        fouriered = torch.cat((freqs.sin(), freqs.cos()), dim = -1)
-
+        fouriered = torch.cat((x, fouriered), dim = -1)
-class PreNorm(nn.Module):
+        return fouriered
-    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)
 
 # building block modules
 
 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()
 
@@ -158,6 +200,7 @@ class ResnetBlock(nn.Module):
         h = self.block1(x, scale_shift = scale_shift)
 
         h = self.block2(h)
+
         return h + self.res_conv(x)
 
 class LinearAttention(nn.Module):
@@ -182,6 +225,8 @@ class LinearAttention(nn.Module):
         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)
@@ -194,6 +239,7 @@ class Attention(nn.Module):
         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)
 
@@ -201,30 +247,18 @@ class Attention(nn.Module):
         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)
-        sim = sim - sim.amax(dim = -1, keepdim = True).detach()
         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
 
-def MLP(dim_in, dim_hidden):
-    return nn.Sequential(
-        Rearrange('... -> ... 1'),
-        nn.Linear(1, dim_hidden),
-        nn.GELU(),
-        nn.LayerNorm(dim_hidden),
-        nn.Linear(dim_hidden, dim_hidden),
-        nn.GELU(),
-        nn.LayerNorm(dim_hidden),
-        nn.Linear(dim_hidden, dim_hidden)
-    )
-
 class Unet(nn.Module):
     def __init__(
         self,
@@ -233,18 +267,23 @@ 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,
-        sinusoidal_cond_mlp = True
+        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.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:]))
@@ -255,17 +294,21 @@ class Unet(nn.Module):
 
         time_dim = dim * 4
 
-        self.sinusoidal_cond_mlp = sinusoidal_cond_mlp
+        self.random_or_learned_sinusoidal_cond = learned_sinusoidal_cond or random_fourier_features
 
-        if sinusoidal_cond_mlp:
+        if self.random_or_learned_sinusoidal_cond:
-            self.time_mlp = nn.Sequential(
+            sinu_pos_emb = RandomOrLearnedSinusoidalPosEmb(learned_sinusoidal_dim, random_fourier_features)
-                SinusoidalPosEmb(dim),
+            fourier_dim = learned_sinusoidal_dim + 1
-                nn.Linear(dim, time_dim),
-                nn.GELU(),
-                nn.Linear(time_dim, time_dim)
-            )
         else:
-            self.time_mlp = MLP(1, time_dim)
+            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
 
@@ -277,10 +320,10 @@ class Unet(nn.Module):
             is_last = ind >= (num_resolutions - 1)
 
             self.downs.append(nn.ModuleList([
-                block_klass(dim_in, dim_out, time_emb_dim = time_dim),
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim),
-                block_klass(dim_out, dim_out, time_emb_dim = time_dim),
+                block_klass(dim_in, dim_in, time_emb_dim = time_dim),
-                Residual(PreNorm(dim_out, LinearAttention(dim_out))),
+                Residual(PreNorm(dim_in, LinearAttention(dim_in))),
-                Downsample(dim_out) if not is_last else nn.Identity()
+                Downsample(dim_in, dim_out) if not is_last else nn.Conv2d(dim_in, dim_out, 3, padding = 1)
             ]))
 
         mid_dim = dims[-1]
@@ -292,21 +335,23 @@ class Unet(nn.Module):
             is_last = ind == (len(in_out) - 1)
 
             self.ups.append(nn.ModuleList([
-                block_klass(dim_out * 2, dim_in, time_emb_dim = time_dim),
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim),
-                block_klass(dim_in, dim_in, time_emb_dim = time_dim),
+                block_klass(dim_out + dim_in, dim_out, time_emb_dim = time_dim),
-                Residual(PreNorm(dim_in, LinearAttention(dim_in))),
+                Residual(PreNorm(dim_out, LinearAttention(dim_out))),
-                Upsample(dim_in) if not is_last else nn.Identity()
+                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_conv = nn.Sequential(
+        self.final_res_block = block_klass(dim * 2, dim, time_emb_dim = time_dim)
-            block_klass(dim * 2, dim),
+        self.final_conv = nn.Conv2d(dim, self.out_dim, 1)
-            nn.Conv2d(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)
 
-    def forward(self, x, time):
         x = self.init_conv(x)
         r = x.clone()
 
@@ -316,9 +361,12 @@ class Unet(nn.Module):
 
         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)
@@ -328,11 +376,16 @@ class Unet(nn.Module):
         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
@@ -355,7 +408,7 @@ def cosine_beta_schedule(timesteps, s = 0.008):
     """
     steps = timesteps + 1
     x = torch.linspace(0, timesteps, steps, dtype = torch.float64)
-    alphas_cumprod = torch.cos(((x / timesteps) + s) / (1 + s) * torch.pi * 0.5) ** 2
+    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)
@@ -363,25 +416,32 @@ def cosine_beta_schedule(timesteps, s = 0.008):
 class GaussianDiffusion(nn.Module):
     def __init__(
         self,
-        denoise_fn,
+        model,
         *,
         image_size,
-        channels = 3,
         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
+        p2_loss_weight_k = 1,
+        ddim_sampling_eta = 1.
     ):
         super().__init__()
-        assert not (type(self) == GaussianDiffusion and denoise_fn.channels != denoise_fn.out_dim)
+        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.self_condition = self.model.self_condition
 
-        self.channels = channels
         self.image_size = image_size
-        self.denoise_fn = denoise_fn
+
         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':
@@ -390,13 +450,21 @@ 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
         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))
@@ -437,6 +505,24 @@ class GaussianDiffusion(nn.Module):
             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 +
@@ -446,49 +532,103 @@ 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 p_mean_variance(self, x, t, clip_denoised: bool):
+    def model_predictions(self, x, t, x_self_cond = None, clip_x_start = False):
-        model_output = self.denoise_fn(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':
-            x_start = self.predict_start_from_noise(x, t = t, noise = model_output)
+            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
-        else:
+            x_start = maybe_clip(x_start)
-            raise ValueError(f'unknown objective {self.objective}')
+            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
+        return model_mean, posterior_variance, posterior_log_variance, x_start
 
     @torch.no_grad()
-    def p_sample(self, x, t, clip_denoised=True):
+    def p_sample(self, x, t: int, x_self_cond = None, clip_denoised = True):
         b, *_, device = *x.shape, x.device
-        model_mean, _, model_log_variance = self.p_mean_variance(x=x, t=t, clip_denoised=clip_denoised)
+        batched_times = torch.full((x.shape[0],), t, device = x.device, dtype = torch.long)
-        noise = torch.randn_like(x)
+        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)
-        # no noise when t == 0
+        noise = torch.randn_like(x) if t > 0 else 0. # no noise if t == 0
-        nonzero_mask = (1 - (t == 0).float()).reshape(b, *((1,) * (len(x.shape) - 1)))
+        pred_img = model_mean + (0.5 * model_log_variance).exp() * noise
-        return model_mean + nonzero_mask * (0.5 * model_log_variance).exp() * noise
+        return pred_img, x_start
 
     @torch.no_grad()
     def p_sample_loop(self, shape):
-        device = self.betas.device
+        batch, device = shape[0], self.betas.device
 
-        b = shape[0]
         img = torch.randn(shape, device=device)
 
-        for i in tqdm(reversed(range(0, self.num_timesteps)), desc='sampling loop time step', total=self.num_timesteps):
+        x_start = None
-            img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))
+
+        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):
-        image_size = self.image_size
+        image_size, channels = self.image_size, self.channels
-        channels = self.channels
+        sample_fn = self.p_sample_loop if not self.is_ddim_sampling else self.ddim_sample
-        return self.p_sample_loop((batch_size, channels, image_size, image_size))
+        return sample_fn((batch_size, channels, image_size, image_size))
 
     @torch.no_grad()
     def interpolate(self, x1, x2, t = None, lam = 0.5):
@@ -497,11 +637,11 @@ 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
@@ -527,13 +667,31 @@ class GaussianDiffusion(nn.Module):
         b, c, h, w = x_start.shape
         noise = default(noise, lambda: torch.randn_like(x_start))
 
-        x = self.q_sample(x_start=x_start, t=t, noise=noise)
+        # noise sample
-        model_out = self.denoise_fn(x, t)
+
+        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}')
 
@@ -553,18 +711,28 @@ class GaussianDiffusion(nn.Module):
 
 # dataset classes
 
-class Dataset(data.Dataset):
+class Dataset(Dataset):
-    def __init__(self, folder, image_size, exts = ['jpg', 'jpeg', 'png'], augment_horizontal_flip = False):
+    def __init__(
+        self,
+        folder,
+        image_size,
+        exts = ['jpg', 'jpeg', 'png', 'tiff'],
+        augment_horizontal_flip = False,
+        convert_image_to = None
+    ):
         super().__init__()
         self.folder = folder
         self.image_size = image_size
         self.paths = [p for ext in exts for p in Path(f'{folder}').glob(f'**/*.{ext}')]
 
-        self.transform = transforms.Compose([
+        maybe_convert_fn = partial(convert_image_to_fn, convert_image_to) if exists(convert_image_to) else nn.Identity()
-            transforms.Resize(image_size),
+
-            transforms.RandomHorizontalFlip() if augment_horizontal_flip else nn.Identity(),
+        self.transform = T.Compose([
-            transforms.CenterCrop(image_size),
+            T.Lambda(maybe_convert_fn),
-            transforms.ToTensor()
+            T.Resize(image_size),
+            T.RandomHorizontalFlip() if augment_horizontal_flip else nn.Identity(),
+            T.CenterCrop(image_size),
+            T.ToTensor()
         ])
 
     def __len__(self):
@@ -583,104 +751,148 @@ class Trainer(object):
         diffusion_model,
         folder,
         *,
-        ema_decay = 0.995,
+        train_batch_size = 16,
-        image_size = 128,
+        gradient_accumulate_every = 1,
-        train_batch_size = 32,
+        augment_horizontal_flip = True,
         train_lr = 1e-4,
         train_num_steps = 100000,
-        gradient_accumulate_every = 2,
+        ema_update_every = 10,
-        amp = False,
+        ema_decay = 0.995,
-        step_start_ema = 2000,
+        adam_betas = (0.9, 0.99),
-        update_ema_every = 10,
         save_and_sample_every = 1000,
+        num_samples = 25,
         results_folder = './results',
-        augment_horizontal_flip = True
+        amp = False,
+        fp16 = False,
+        split_batches = True,
+        convert_image_to = None
     ):
         super().__init__()
-        self.model = diffusion_model
-        self.ema = EMA(ema_decay)
-        self.ema_model = copy.deepcopy(self.model)
-        self.update_ema_every = update_ema_every
 
-        self.step_start_ema = step_start_ema
+        self.accelerator = Accelerator(
+            split_batches = split_batches,
+            mixed_precision = 'fp16' if fp16 else 'no'
+        )
+
+        self.accelerator.native_amp = amp
+
+        self.model = diffusion_model
+
+        assert has_int_squareroot(num_samples), 'number of samples must have an integer square root'
+        self.num_samples = num_samples
         self.save_and_sample_every = save_and_sample_every
 
         self.batch_size = train_batch_size
-        self.image_size = diffusion_model.image_size
         self.gradient_accumulate_every = gradient_accumulate_every
-        self.train_num_steps = train_num_steps
 
-        self.ds = Dataset(folder, image_size, augment_horizontal_flip = augment_horizontal_flip)
+        self.train_num_steps = train_num_steps
-        self.dl = cycle(data.DataLoader(self.ds, batch_size = train_batch_size, shuffle = True, pin_memory = True, num_workers = cpu_count()))
+        self.image_size = diffusion_model.image_size
-        self.opt = Adam(diffusion_model.parameters(), lr=train_lr)
+
+        # dataset and dataloader
+
+        self.ds = Dataset(folder, self.image_size, augment_horizontal_flip = augment_horizontal_flip, convert_image_to = convert_image_to)
+        dl = DataLoader(self.ds, batch_size = train_batch_size, shuffle = True, pin_memory = True, num_workers = cpu_count())
+
+        dl = self.accelerator.prepare(dl)
+        self.dl = cycle(dl)
+
+        # optimizer
+
+        self.opt = Adam(diffusion_model.parameters(), lr = train_lr, betas = adam_betas)
+
+        # for logging results in a folder periodically
+
+        if self.accelerator.is_main_process:
+            self.ema = EMA(diffusion_model, beta = ema_decay, update_every = ema_update_every)
+
+            self.results_folder = Path(results_folder)
+            self.results_folder.mkdir(exist_ok = True)
+
+        # step counter state
 
         self.step = 0
 
-        self.amp = amp
+        # prepare model, dataloader, optimizer with accelerator
-        self.scaler = GradScaler(enabled = amp)
 
-        self.results_folder = Path(results_folder)
+        self.model, self.opt = self.accelerator.prepare(self.model, self.opt)
-        self.results_folder.mkdir(exist_ok = True)
-
-        self.reset_parameters()
-
-    def reset_parameters(self):
-        self.ema_model.load_state_dict(self.model.state_dict())
-
-    def step_ema(self):
-        if self.step < self.step_start_ema:
-            self.reset_parameters()
-            return
-        self.ema.update_model_average(self.ema_model, self.model)
 
     def save(self, milestone):
+        if not self.accelerator.is_local_main_process:
+            return
+
         data = {
             'step': self.step,
-            'model': self.model.state_dict(),
+            'model': self.accelerator.get_state_dict(self.model),
-            'ema': self.ema_model.state_dict(),
+            'opt': self.opt.state_dict(),
-            'scaler': self.scaler.state_dict()
+            'ema': self.ema.state_dict(),
+            'scaler': self.accelerator.scaler.state_dict() if exists(self.accelerator.scaler) else None
         }
+
         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'])
 
         self.step = data['step']
-        self.model.load_state_dict(data['model'])
+        self.opt.load_state_dict(data['opt'])
-        self.ema_model.load_state_dict(data['ema'])
+        self.ema.load_state_dict(data['ema'])
-        self.scaler.load_state_dict(data['scaler'])
+
+        if exists(self.accelerator.scaler) and exists(data['scaler']):
+            self.accelerator.scaler.load_state_dict(data['scaler'])
 
     def train(self):
-        with tqdm(initial = self.step, total = self.train_num_steps) as pbar:
+        accelerator = self.accelerator
+        device = accelerator.device
+
+        with tqdm(initial = self.step, total = self.train_num_steps, disable = not accelerator.is_main_process) as pbar:
 
             while self.step < self.train_num_steps:
-                for i in range(self.gradient_accumulate_every):
-                    data = next(self.dl).cuda()
 
-                    with autocast(enabled = self.amp):
+                total_loss = 0.
+
+                for _ in range(self.gradient_accumulate_every):
+                    data = next(self.dl).to(device)
+
+                    with self.accelerator.autocast():
                         loss = self.model(data)
-                        self.scaler.scale(loss / self.gradient_accumulate_every).backward()
+                        loss = loss / self.gradient_accumulate_every
+                        total_loss += loss.item()
 
-                    pbar.set_description(f'loss: {loss.item():.4f}')
+                    self.accelerator.backward(loss)
 
-                self.scaler.step(self.opt)
+                accelerator.clip_grad_norm_(self.model.parameters(), 1.0)
-                self.scaler.update()
+                pbar.set_description(f'loss: {total_loss:.4f}')
+
+                accelerator.wait_for_everyone()
+
+                self.opt.step()
                 self.opt.zero_grad()
 
-                if self.step % self.update_ema_every == 0:
+                accelerator.wait_for_everyone()
-                    self.step_ema()
-
-                if self.step != 0 and self.step % self.save_and_sample_every == 0:
-                    self.ema_model.eval()
-
-                    milestone = self.step // self.save_and_sample_every
-                    batches = num_to_groups(36, self.batch_size)
-                    all_images_list = list(map(lambda n: self.ema_model.sample(batch_size=n), batches))
-                    all_images = torch.cat(all_images_list, dim=0)
-                    utils.save_image(all_images, str(self.results_folder / f'sample-{milestone}.png'), nrow = 6)
-                    self.save(milestone)
 
                 self.step += 1
+                if accelerator.is_main_process:
+                    self.ema.to(device)
+                    self.ema.update()
+
+                    if self.step != 0 and self.step % self.save_and_sample_every == 0:
+                        self.ema.ema_model.eval()
+
+                        with torch.no_grad():
+                            milestone = self.step // self.save_and_sample_every
+                            batches = num_to_groups(self.num_samples, self.batch_size)
+                            all_images_list = list(map(lambda n: self.ema.ema_model.sample(batch_size=n), batches))
+
+                        all_images = torch.cat(all_images_list, dim = 0)
+                        utils.save_image(all_images, str(self.results_folder / f'sample-{milestone}.png'), nrow = int(math.sqrt(self.num_samples)))
+                        self.save(milestone)
+
                 pbar.update(1)
 
-        print('training complete')
+        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

@@ -0,0 +1,240 @@
+from math import sqrt
+from random import random
+import torch
+from torch import nn, einsum
+import torch.nn.functional as F
+
+from tqdm import tqdm
+from einops import rearrange, repeat, reduce
+
+# 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
+
+# tensor helpers
+
+def log(t, eps = 1e-20):
+    return torch.log(t.clamp(min = eps))
+
+# 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
+
+# main class
+
+class ElucidatedDiffusion(nn.Module):
+    def __init__(
+        self,
+        net,
+        *,
+        image_size,
+        channels = 3,
+        num_sample_steps = 32, # number of sampling steps
+        sigma_min = 0.002,     # min noise level
+        sigma_max = 80,        # max noise level
+        sigma_data = 0.5,      # standard deviation of data distribution
+        rho = 7,               # controls the sampling schedule
+        P_mean = -1.2,         # mean of log-normal distribution from which noise is drawn for training
+        P_std = 1.2,           # standard deviation of log-normal distribution from which noise is drawn for training
+        S_churn = 80,          # parameters for stochastic sampling - depends on dataset, Table 5 in apper
+        S_tmin = 0.05,
+        S_tmax = 50,
+        S_noise = 1.003,
+    ):
+        super().__init__()
+        assert net.random_or_learned_sinusoidal_cond
+        self.self_condition = net.self_condition
+
+        self.net = net
+
+        # image dimensions
+
+        self.channels = channels
+        self.image_size = image_size
+
+        # parameters
+
+        self.sigma_min = sigma_min
+        self.sigma_max = sigma_max
+        self.sigma_data = sigma_data
+
+        self.rho = rho
+
+        self.P_mean = P_mean
+        self.P_std = P_std
+
+        self.num_sample_steps = num_sample_steps  # otherwise known as N in the paper
+
+        self.S_churn = S_churn
+        self.S_tmin = S_tmin
+        self.S_tmax = S_tmax
+        self.S_noise = S_noise
+
+    @property
+    def device(self):
+        return next(self.net.parameters()).device
+
+    # derived preconditioning params - Table 1
+
+    def c_skip(self, sigma):
+        return (self.sigma_data ** 2) / (sigma ** 2 + self.sigma_data ** 2)
+
+    def c_out(self, sigma):
+        return sigma * self.sigma_data * (self.sigma_data ** 2 + sigma ** 2) ** -0.5
+
+    def c_in(self, sigma):
+        return 1 * (sigma ** 2 + self.sigma_data ** 2) ** -0.5
+
+    def c_noise(self, sigma):
+        return log(sigma) * 0.25
+
+    # preconditioned network output
+    # equation (7) in the paper
+
+    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):
+            sigma = torch.full((batch,), sigma, device = device)
+
+        padded_sigma = rearrange(sigma, 'b -> b 1 1 1')
+
+        net_out = self.net(
+            self.c_in(padded_sigma) * noised_images,
+            self.c_noise(sigma),
+            self_cond
+        )
+
+        out = self.c_skip(padded_sigma) * noised_images +  self.c_out(padded_sigma) * net_out
+
+        if clamp:
+            out = out.clamp(-1., 1.)
+
+        return out
+
+    # sampling
+
+    # sample schedule
+    # equation (5) in the paper
+
+    def sample_schedule(self, num_sample_steps = None):
+        num_sample_steps = default(num_sample_steps, self.num_sample_steps)
+
+        N = num_sample_steps
+        inv_rho = 1 / self.rho
+
+        steps = torch.arange(num_sample_steps, device = self.device, dtype = torch.float32)
+        sigmas = (self.sigma_max ** inv_rho + steps / (N - 1) * (self.sigma_min ** inv_rho - self.sigma_max ** inv_rho)) ** self.rho
+
+        sigmas = F.pad(sigmas, (0, 1), value = 0.) # last step is sigma value of 0.
+        return sigmas
+
+    @torch.no_grad()
+    def sample(self, batch_size = 16, num_sample_steps = None, clamp = True):
+        num_sample_steps = default(num_sample_steps, self.num_sample_steps)
+
+        shape = (batch_size, self.channels, self.image_size, self.image_size)
+
+        # get the schedule, which is returned as (sigma, gamma) tuple, and pair up with the next sigma and gamma
+
+        sigmas = self.sample_schedule(num_sample_steps)
+
+        gammas = torch.where(
+            (sigmas >= self.S_tmin) & (sigmas <= self.S_tmax),
+            min(self.S_churn / num_sample_steps, sqrt(2) - 1),
+            0.
+        )
+
+        sigmas_and_gammas = list(zip(sigmas[:-1], sigmas[1:], gammas[:-1]))
+
+        # images is noise at the beginning
+
+        init_sigma = sigmas[0]
+
+        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'):
+            sigma, sigma_next, gamma = map(lambda t: t.item(), (sigma, sigma_next, gamma))
+
+            eps = self.S_noise * torch.randn(shape, device = self.device) # stochastic sampling
+
+            sigma_hat = sigma + gamma * sigma
+            images_hat = images + sqrt(sigma_hat ** 2 - sigma ** 2) * eps
+
+            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
+
+            # second order correction, if not the last timestep
+
+            if sigma_next != 0:
+                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)
+
+    # training
+
+    def loss_weight(self, sigma):
+        return (sigma ** 2 + self.sigma_data ** 2) * (sigma * self.sigma_data) ** -2
+
+    def noise_distribution(self, batch_size):
+        return (self.P_mean + self.P_std * torch.randn((batch_size,), device = self.device)).exp()
+
+    def forward(self, images):
+        batch_size, c, h, w, device, image_size, channels = *images.shape, images.device, self.image_size, self.channels
+
+        assert h == image_size and w == image_size, f'height and width of image must be {image_size}'
+        assert c == channels, 'mismatch of image channels'
+
+        images = normalize_to_neg_one_to_one(images)
+
+        sigmas = self.noise_distribution(batch_size)
+        padded_sigmas = rearrange(sigmas, 'b -> b 1 1 1')
+
+        noise = torch.randn_like(images)
+
+        noised_images = images + padded_sigmas * noise  # alphas are 1. in the paper
+
+        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')
+
+        losses = losses * self.loss_weight(sigmas)
+
+        return losses.mean()

denoising_diffusion_pytorch/learned_gaussian_diffusion.py

@@ -1,4 +1,5 @@
 import torch
+from collections import namedtuple
 from math import pi, sqrt, log as ln
 from inspect import isfunction
 from torch import nn, einsum
@@ -10,6 +11,8 @@ from denoising_diffusion_pytorch.denoising_diffusion_pytorch import GaussianDiff
 
 NAT = 1. / ln(2)
 
+ModelPrediction = namedtuple('ModelPrediction', ['pred_noise', 'pred_x_start', 'pred_variance'])
+
 # helper functions
 
 def exists(x):
@@ -22,7 +25,7 @@ def default(val, d):
 
 # tensor helpers
 
-def log(t, eps = 1e-12):
+def log(t, eps = 1e-15):
     return torch.log(t.clamp(min = eps))
 
 def meanflat(x):
@@ -67,17 +70,33 @@ def discretized_gaussian_log_likelihood(x, *, means, log_scales, thres = 0.999):
 class LearnedGaussianDiffusion(GaussianDiffusion):
     def __init__(
         self,
-        denoise_fn,
+        model,
         vb_loss_weight = 0.001,  # lambda was 0.001 in the paper
         *args,
         **kwargs
     ):
-        super().__init__(denoise_fn, *args, **kwargs)
+        super().__init__(model, *args, **kwargs)
-        assert denoise_fn.out_dim == (denoise_fn.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 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):
+        model_output = self.model(x, t)
+        model_output, pred_variance = model_output.chunk(2, dim = 1)
+
+        if self.objective == 'pred_noise':
+            pred_noise = model_output
+            x_start = self.predict_start_from_noise(x, t, model_output)
+
+        elif self.objective == 'pred_x0':
+            pred_noise = self.predict_noise_from_start(x, t, model_output)
+            x_start = model_output
+
+        return ModelPrediction(pred_noise, x_start, pred_variance)
+
     def p_mean_variance(self, *, x, t, clip_denoised, model_output = None):
-        model_output = default(model_output, lambda: self.denoise_fn(x, t))
+        model_output = default(model_output, lambda: self.model(x, t))
         pred_noise, var_interp_frac_unnormalized = model_output.chunk(2, dim = 1)
 
         min_log = extract(self.posterior_log_variance_clipped, t, x.shape)
@@ -102,7 +121,7 @@ class LearnedGaussianDiffusion(GaussianDiffusion):
 
         # model output
 
-        model_output = self.denoise_fn(x_t, t)
+        model_output = self.model(x_t, t)
 
         # calculating kl loss for learned variance (interpolation)
 

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

@@ -22,22 +22,24 @@ def default(val, d):
 class WeightedObjectiveGaussianDiffusion(GaussianDiffusion):
     def __init__(
         self,
-        denoise_fn,
+        model,
         *args,
         pred_noise_loss_weight = 0.1,
         pred_x_start_loss_weight = 0.1,
         **kwargs
     ):
-        super().__init__(denoise_fn, *args, **kwargs)
+        super().__init__(model, *args, **kwargs)
-        channels = denoise_fn.channels
+        channels = model.channels
-        assert denoise_fn.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 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)
         self.pred_noise_loss_weight = pred_noise_loss_weight
         self.pred_x_start_loss_weight = pred_x_start_loss_weight
 
     def p_mean_variance(self, *, x, t, clip_denoised, model_output = None):
-        model_output = self.denoise_fn(x, t)
+        model_output = self.model(x, t)
 
         pred_noise, pred_x_start, weights = model_output.split(self.split_dims, dim = 1)
         normalized_weights = weights.softmax(dim = 1)
@@ -58,7 +60,7 @@ class WeightedObjectiveGaussianDiffusion(GaussianDiffusion):
         noise = default(noise, lambda: torch.randn_like(x_start))
         x_t = self.q_sample(x_start = x_start, t = t, noise = noise)
 
-        model_output = self.denoise_fn(x_t, t)
+        model_output = self.model(x_t, t)
         pred_noise, pred_x_start, weights = model_output.split(self.split_dims, dim = 1)
 
         # get loss for predicted noise and x_start

setup.py

@@ -3,7 +3,7 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.19.2',
+  version = '0.31.0',
   license='MIT',
   description = 'Denoising Diffusion Probabilistic Models - Pytorch',
   author = 'Phil Wang',
@@ -15,7 +15,9 @@ setup(
     'generative models'
   ],
   install_requires=[
+    'accelerate',
     'einops',
+    'ema-pytorch',
     'pillow',
     'torch',
     'torchvision',
@@ -28,4 +30,4 @@ setup(
     'License :: OSI Approved :: MIT License',
     'Programming Language :: Python :: 3.6',
   ],
-)
+)