higher default learning rate

updated citation in README

.gitignore

@@ -1,3 +1,6 @@
+# Generation results
+results/
+
 # Byte-compiled / optimized / DLL files
 __pycache__/
 *.py[cod]

README.md

@@ -1,6 +1,14 @@
-## Denoising Diffusion Probabilistic Model, in Pytorch (wip)
+<img src="./denoising-diffusion.png" width="500px"></img>
 
-Implementation of <a href="https://arxiv.org/abs/2006.11239">Denoising Diffusion Probabilistic Model</a> in Pytorch.
+## Denoising Diffusion Probabilistic Model, in Pytorch
+
+Implementation of <a href="https://arxiv.org/abs/2006.11239">Denoising Diffusion Probabilistic Model</a> in Pytorch. It is a new approach to generative modeling that may <a href="https://ajolicoeur.wordpress.com/the-new-contender-to-gans-score-matching-with-langevin-sampling/">have the potential</a> to rival GANs. It uses denoising score matching to estimate the gradient of the data distribution, followed by Langevin sampling to sample from the true distribution.
+
+This implementation was transcribed from the official Tensorflow version <a href="https://github.com/hojonathanho/diffusion">here</a>
+
+<img src="./sample.png" width="500px"><img>
+
+[![PyPI version](https://badge.fury.io/py/denoising-diffusion-pytorch.svg)](https://badge.fury.io/py/denoising-diffusion-pytorch)
 
 ## Install
 
@@ -21,41 +29,82 @@ model = Unet(
 
 diffusion = GaussianDiffusion(
     model,
-    beta_start = 0.0001,
-    beta_end = 0.02,
-    num_diffusion_timesteps = 1000,   # number of steps
-    loss_type = 'l1'                  # L1 or L2 (wavegrad paper claims l1 is better?)
+    image_size = 128,
+    timesteps = 1000,   # number of steps
+    loss_type = 'l1'    # L1 or L2
 )
 
-training_images = torch.randn(8, 3, 128, 128)
+training_images = torch.randn(8, 3, 128, 128) # your images need to be normalized from a range of -1 to +1
 loss = diffusion(training_images)
 loss.backward()
 # after a lot of training
 
-sampled_images = diffusion.p_sample_loop((1, 3, 128, 128))
-sampled_images.shape # (1, 3, 128, 128)
+sampled_images = diffusion.sample(batch_size = 4)
+sampled_images.shape # (4, 3, 128, 128)
 ```
 
+Or, if you simply want to pass in a folder name and the desired image dimensions, you can use the `Trainer` class to easily train a model.
+
+```python
+from denoising_diffusion_pytorch import Unet, GaussianDiffusion, Trainer
+
+model = Unet(
+    dim = 64,
+    dim_mults = (1, 2, 4, 8)
+).cuda()
+
+diffusion = GaussianDiffusion(
+    model,
+    image_size = 128,
+    timesteps = 1000,   # number of steps
+    loss_type = 'l1'    # L1 or L2
+).cuda()
+
+trainer = Trainer(
+    diffusion,
+    'path/to/your/images',
+    train_batch_size = 32,
+    train_lr = 1e-4,
+    train_num_steps = 700000,         # total training steps
+    gradient_accumulate_every = 2,    # gradient accumulation steps
+    ema_decay = 0.995,                # exponential moving average decay
+    amp = True                        # turn on mixed precision
+)
+
+trainer.train()
+```
+
+Samples and model checkpoints will be logged to `./results` periodically
+
 ## Citations
 
 ```bibtex
-@misc{ho2020denoising,
-    title={Denoising Diffusion Probabilistic Models},
-    author={Jonathan Ho and Ajay Jain and Pieter Abbeel},
-    year={2020},
-    eprint={2006.11239},
-    archivePrefix={arXiv},
-    primaryClass={cs.LG}
+@inproceedings{NEURIPS2020_4c5bcfec,
+    author      = {Ho, Jonathan and Jain, Ajay and Abbeel, Pieter},
+    booktitle   = {Advances in Neural Information Processing Systems},
+    editor      = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
+    pages       = {6840--6851},
+    publisher   = {Curran Associates, Inc.},
+    title       = {Denoising Diffusion Probabilistic Models},
+    url         = {https://proceedings.neurips.cc/paper/2020/file/4c5bcfec8584af0d967f1ab10179ca4b-Paper.pdf},
+    volume      = {33},
+    year        = {2020}
 }
 ```
 
 ```bibtex
-@misc{chen2020wavegrad,
-    title={WaveGrad: Estimating Gradients for Waveform Generation},
-    author={Nanxin Chen and Yu Zhang and Heiga Zen and Ron J. Weiss and Mohammad Norouzi and William Chan},
-    year={2020},
-    eprint={2009.00713},
-    archivePrefix={arXiv},
-    primaryClass={eess.AS}
+@InProceedings{pmlr-v139-nichol21a,
+    title       = {Improved Denoising Diffusion Probabilistic Models},
+    author      = {Nichol, Alexander Quinn and Dhariwal, Prafulla},
+    booktitle   = {Proceedings of the 38th International Conference on Machine Learning},
+    pages       = {8162--8171},
+    year        = {2021},
+    editor      = {Meila, Marina and Zhang, Tong},
+    volume      = {139},
+    series      = {Proceedings of Machine Learning Research},
+    month       = {18--24 Jul},
+    publisher   = {PMLR},
+    pdf         = {http://proceedings.mlr.press/v139/nichol21a/nichol21a.pdf},
+    url         = {https://proceedings.mlr.press/v139/nichol21a.html},
 }
 ```

denoising_diffusion_pytorch/__init__.py

@@ -1 +1,4 @@
-from denoising_diffusion_pytorch.denoising_diffusion_pytorch import GaussianDiffusion, Unet
+from denoising_diffusion_pytorch.denoising_diffusion_pytorch import GaussianDiffusion, Unet, Trainer
+
+from denoising_diffusion_pytorch.learned_gaussian_diffusion import LearnedGaussianDiffusion
+from denoising_diffusion_pytorch.weighted_objective_gaussian_diffusion import WeightedObjectiveGaussianDiffusion

denoising_diffusion_pytorch/denoising_diffusion_pytorch.py

@@ -1,11 +1,19 @@
 import math
+import copy
 import torch
-from inspect import isfunction
-from functools import partial
 from torch import nn, einsum
 import torch.nn.functional as F
+from inspect import isfunction
+from functools import partial
+
+from torch.utils import data
+from torch.cuda.amp import autocast, GradScaler
+
+from pathlib import Path
+from torch.optim import Adam
+from torchvision import transforms, utils
+from PIL import Image
 
-import numpy as np
 from tqdm import tqdm
 from einops import rearrange
 
@@ -19,11 +27,42 @@ def default(val, d):
         return val
     return d() if isfunction(d) else d
 
-def normal_kl(mean1, logvar1, mean2, logvar2):
-    return 0.5 * (-1. + logvar2 - logvar1 + torch.exp(logvar1 - logvar2) + torch.exp(-logvar2) * (mean1 - mean2) ** 2)
+def cycle(dl):
+    while True:
+        for data in dl:
+            yield data
+
+def num_to_groups(num, divisor):
+    groups = num // divisor
+    remainder = num % divisor
+    arr = [divisor] * groups
+    if remainder > 0:
+        arr.append(remainder)
+    return arr
+
+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 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__()
@@ -46,98 +85,163 @@ class SinusoidalPosEmb(nn.Module):
         emb = torch.cat((emb.sin(), emb.cos()), dim=-1)
         return emb
 
-class Mish(nn.Module):
-    def forward(self, x):
-        return x * torch.tanh(F.softplus(x))
+def Upsample(dim):
+    return nn.ConvTranspose2d(dim, dim, 4, 2, 1)
 
-class Upsample(nn.Module):
-    def __init__(self, dim):
+def Downsample(dim):
+    return nn.Conv2d(dim, dim, 4, 2, 1)
+
+class LayerNorm(nn.Module):
+    def __init__(self, dim, eps = 1e-5):
         super().__init__()
-        self.conv = nn.ConvTranspose2d(dim, dim, 4, 2, 1)
+        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):
-        return self.conv(x)
+        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
 
-class Downsample(nn.Module):
-    def __init__(self, dim):
+class PreNorm(nn.Module):
+    def __init__(self, dim, fn):
         super().__init__()
-        self.conv = nn.Conv2d(dim, dim, 3, 2, 1)
+        self.fn = fn
+        self.norm = LayerNorm(dim)
 
     def forward(self, x):
-        return self.conv(x)
-
-class Rezero(nn.Module):
-    def __init__(self, dim):
-        super().__init__()
-        self.g = nn.Parameter(torch.zeros(1))
-
-    def forward(self, x):
-        return x * self.g
+        x = self.norm(x)
+        return self.fn(x)
 
 # building block modules
 
 class Block(nn.Module):
-    def __init__(self, dim, dim_out, groups = 32):
+    def __init__(self, dim, dim_out, groups = 8):
         super().__init__()
         self.block = nn.Sequential(
-            nn.Conv2d(dim, dim_out, 3, padding=1),
+            nn.Conv2d(dim, dim_out, 3, padding = 1),
             nn.GroupNorm(groups, dim_out),
-            Mish()
+            nn.SiLU()
         )
     def forward(self, x):
         return self.block(x)
 
 class ResnetBlock(nn.Module):
-    def __init__(self, dim, dim_out, *, time_emb_dim, groups = 32):
+    def __init__(self, dim, dim_out, *, time_emb_dim = None, groups = 8):
         super().__init__()
         self.mlp = nn.Sequential(
-            Mish(),
+            nn.SiLU(),
             nn.Linear(time_emb_dim, dim_out)
-        )
+        ) if exists(time_emb_dim) else None
 
-        self.block1 = Block(dim, dim_out)
-        self.block2 = Block(dim_out, dim_out)
+        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):
+    def forward(self, x, time_emb = None):
         h = self.block1(x)
-        h += self.mlp(time_emb)[:, :, None, None]
+
+        if exists(self.mlp) and exists(time_emb):
+            time_emb = self.mlp(time_emb)
+            h = rearrange(time_emb, 'b c -> b c 1 1') + h
+
         h = self.block2(h)
         return h + self.res_conv(x)
 
 class LinearAttention(nn.Module):
-    def __init__(self, dim, heads = 8, dim_head = 32):
+    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, 1, bias = False)
+        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
+        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)
-        q, k, v = rearrange(qkv, 'b (qkv heads c) h w -> qkv b heads c (h w)', heads = self.heads)
-        q = q.softmax(dim=-2)
-        k = k.softmax(dim=-1)
-        context = torch.einsum('bhdn,bhen->bhde', k, v)
-        out = torch.einsum('bhde,bhdn->bhen', context, q)
-        out = rearrange(out, 'b heads c (h w) -> b (heads c) h w', heads=self.heads, h=h, w=w)
+        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
 
 class Unet(nn.Module):
-    def __init__(self, dim, out_dim = None, dim_mults=(1, 2, 4, 8), groups = 32):
+    def __init__(
+        self,
+        dim,
+        init_dim = None,
+        out_dim = None,
+        dim_mults=(1, 2, 4, 8),
+        channels = 3,
+        with_time_emb = True,
+        resnet_block_groups = 8,
+        learned_variance = False
+    ):
         super().__init__()
-        dims = [3, *map(lambda m: dim * m, dim_mults)]
+
+        # determine dimensions
+
+        self.channels = channels
+
+        init_dim = default(init_dim, dim // 3 * 2)
+        self.init_conv = nn.Conv2d(channels, init_dim, 7, padding = 3)
+
+        dims = [init_dim, *map(lambda m: dim * m, dim_mults)]
         in_out = list(zip(dims[:-1], dims[1:]))
 
-        self.time_pos_emb = SinusoidalPosEmb(dim)
-        self.mlp = nn.Sequential(
-            nn.Linear(dim, dim * 4),
-            Mish(),
-            nn.Linear(dim * 4, dim)
-        )
+        block_klass = partial(ResnetBlock, groups = resnet_block_groups)
+
+        # time embeddings
+
+        if with_time_emb:
+            time_dim = dim * 4
+            self.time_mlp = nn.Sequential(
+                SinusoidalPosEmb(dim),
+                nn.Linear(dim, time_dim),
+                nn.GELU(),
+                nn.Linear(time_dim, time_dim)
+            )
+        else:
+            time_dim = None
+            self.time_mlp = None
+
+        # layers
 
         self.downs = nn.ModuleList([])
         self.ups = nn.ModuleList([])
@@ -147,39 +251,45 @@ class Unet(nn.Module):
             is_last = ind >= (num_resolutions - 1)
 
             self.downs.append(nn.ModuleList([
-                ResnetBlock(dim_in, dim_out, time_emb_dim = dim),
-                Residual(Rezero(LinearAttention(dim_out))),
+                block_klass(dim_in, dim_out, time_emb_dim = time_dim),
+                block_klass(dim_out, dim_out, time_emb_dim = time_dim),
+                Residual(PreNorm(dim_out, LinearAttention(dim_out))),
                 Downsample(dim_out) if not is_last else nn.Identity()
             ]))
 
         mid_dim = dims[-1]
-        self.mid_block1 = ResnetBlock(mid_dim, mid_dim, time_emb_dim = dim)
-        self.mid_attn = Residual(Rezero(LinearAttention(mid_dim)))
-        self.mid_block2 = ResnetBlock(mid_dim, mid_dim, time_emb_dim = dim)
+        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[1:])):
             is_last = ind >= (num_resolutions - 1)
 
             self.ups.append(nn.ModuleList([
-                ResnetBlock(dim_out * 2, dim_in, time_emb_dim = dim),
-                Residual(Rezero(LinearAttention(dim_in))),
+                block_klass(dim_out * 2, 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))),
                 Upsample(dim_in) if not is_last else nn.Identity()
             ]))
 
-        out_dim = default(out_dim, 3)
+        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(
-            Block(dim, dim),
-            nn.Conv2d(dim, out_dim, 1)
+            block_klass(dim, dim),
+            nn.Conv2d(dim, self.out_dim, 1)
         )
 
     def forward(self, x, time):
-        t = self.time_pos_emb(time)
-        t = self.mlp(t)
+        x = self.init_conv(x)
+
+        t = self.time_mlp(time) if exists(self.time_mlp) else None
 
         h = []
 
-        for resnet, attn, downsample in self.downs:
-            x = resnet(x, t)
+        for block1, block2, attn, downsample in self.downs:
+            x = block1(x, t)
+            x = block2(x, t)
             x = attn(x)
             h.append(x)
             x = downsample(x)
@@ -188,9 +298,10 @@ class Unet(nn.Module):
         x = self.mid_attn(x)
         x = self.mid_block2(x, t)
 
-        for resnet, attn, upsample in self.ups:
+        for block1, block2, attn, upsample in self.ups:
             x = torch.cat((x, h.pop()), dim=1)
-            x = resnet(x, t)
+            x = block1(x, t)
+            x = block2(x, t)
             x = attn(x)
             x = upsample(x)
 
@@ -208,49 +319,76 @@ def noise_like(shape, device, repeat=False):
     noise = lambda: torch.randn(shape, device=device)
     return repeat_noise() if repeat else noise()
 
+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) * torch.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, denoise_fn, beta_start=0.0001, beta_end=0.02, num_diffusion_timesteps=1000, loss_type='l1'):
+    def __init__(
+        self,
+        denoise_fn,
+        *,
+        image_size,
+        channels = 3,
+        timesteps = 1000,
+        loss_type = 'l1',
+        objective = 'pred_noise'
+    ):
         super().__init__()
+        assert not (type(self) == GaussianDiffusion and denoise_fn.channels != denoise_fn.out_dim)
+
+        self.channels = channels
+        self.image_size = image_size
         self.denoise_fn = denoise_fn
+        self.objective = objective
+
+        betas = cosine_beta_schedule(timesteps)
+
+        alphas = 1. - betas
+        alphas_cumprod = torch.cumprod(alphas, axis=0)
+        alphas_cumprod_prev = F.pad(alphas_cumprod[:-1], (1, 0), value = 1.)
 
-        self.np_betas = betas = np.linspace(beta_start, beta_end, num_diffusion_timesteps).astype(np.float64)
         timesteps, = betas.shape
         self.num_timesteps = int(timesteps)
         self.loss_type = loss_type
 
-        alphas = 1. - betas
-        alphas_cumprod = np.cumprod(alphas, axis=0)
-        alphas_cumprod_prev = np.append(1., alphas_cumprod[:-1])
+        # helper function to register buffer from float64 to float32
 
-        to_torch = partial(torch.tensor, dtype=torch.float32)
+        register_buffer = lambda name, val: self.register_buffer(name, val.to(torch.float32))
 
-        self.register_buffer('betas', to_torch(betas))
-        self.register_buffer('alphas_cumprod', to_torch(alphas_cumprod))
-        self.register_buffer('alphas_cumprod_prev', to_torch(alphas_cumprod_prev))
+        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
-        self.register_buffer('sqrt_alphas_cumprod', to_torch(np.sqrt(alphas_cumprod)))
-        self.register_buffer('sqrt_one_minus_alphas_cumprod', to_torch(np.sqrt(1. - alphas_cumprod)))
-        self.register_buffer('log_one_minus_alphas_cumprod', to_torch(np.log(1. - alphas_cumprod)))
-        self.register_buffer('sqrt_recip_alphas_cumprod', to_torch(np.sqrt(1. / alphas_cumprod)))
-        self.register_buffer('sqrt_recipm1_alphas_cumprod', to_torch(np.sqrt(1. / alphas_cumprod - 1)))
+
+        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)
-        self.register_buffer('posterior_variance', to_torch(posterior_variance))
-        # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain
-        self.register_buffer('posterior_log_variance_clipped', to_torch(np.log(np.maximum(posterior_variance, 1e-20))))
-        self.register_buffer('posterior_mean_coef1', to_torch(
-            betas * np.sqrt(alphas_cumprod_prev) / (1. - alphas_cumprod)))
-        self.register_buffer('posterior_mean_coef2', to_torch(
-            (1. - alphas_cumprod_prev) * np.sqrt(alphas) / (1. - alphas_cumprod)))
 
-    def q_mean_variance(self, x_start, t):
-        mean = extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
-        variance = extract(1. - self.alphas_cumprod, t, x_start.shape)
-        log_variance = extract(self.log_one_minus_alphas_cumprod, t, x_start.shape)
-        return mean, variance, log_variance
+        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))
 
     def predict_start_from_noise(self, x_t, t, noise):
         return (
@@ -268,12 +406,19 @@ class GaussianDiffusion(nn.Module):
         return posterior_mean, posterior_variance, posterior_log_variance_clipped
 
     def p_mean_variance(self, x, t, clip_denoised: bool):
-        x_recon = self.predict_start_from_noise(x, t=t, noise=self.denoise_fn(x, t))
+        model_output = self.denoise_fn(x, t)
+
+        if self.objective == 'pred_noise':
+            x_start = self.predict_start_from_noise(x, t = t, noise = model_output)
+        elif self.objective == 'pred_x0':
+            x_start = model_output
+        else:
+            raise ValueError(f'unknown objective {self.objective}')
 
         if clip_denoised:
-            x_recon.clamp_(-1., 1.)
+            x_start.clamp_(-1., 1.)
 
-        model_mean, posterior_variance, posterior_log_variance = self.q_posterior(x_start=x_recon, x_t=x, t=t)
+        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
 
     @torch.no_grad()
@@ -294,6 +439,30 @@ class GaussianDiffusion(nn.Module):
 
         for i in tqdm(reversed(range(0, self.num_timesteps)), desc='sampling loop time step', total=self.num_timesteps):
             img = self.p_sample(img, torch.full((b,), i, device=device, dtype=torch.long))
+
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def sample(self, batch_size = 16):
+        image_size = self.image_size
+        channels = self.channels
+        return self.p_sample_loop((batch_size, channels, image_size, image_size))
+
+    @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):
@@ -304,23 +473,169 @@ class GaussianDiffusion(nn.Module):
             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, h, w = x_start.shape
         noise = default(noise, lambda: torch.randn_like(x_start))
 
-        x_noisy = self.q_sample(x_start=x_start, t=t, noise=noise)
-        x_recon = self.denoise_fn(x_noisy, t)
+        x = self.q_sample(x_start=x_start, t=t, noise=noise)
+        model_out = self.denoise_fn(x, t)
 
-        if self.loss_type == 'l1':
-            loss = (noise - x_recon).abs().mean()
-        elif self.loss_type == 'l2':
-            loss = F.mse_loss(noise, x_recon)
+        if self.objective == 'pred_noise':
+            target = noise
+        elif self.objective == 'pred_x0':
+            target = x_start
         else:
-            raise NotImplementedError()
+            raise ValueError(f'unknown objective {self.objective}')
 
+        loss = self.loss_fn(model_out, target)
         return loss
 
-    def forward(self, x, *args, **kwargs):
-        b, *_, device = *x.shape, x.device
+    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()
-        return self.p_losses(x, t, *args, **kwargs)
+
+        img = normalize_to_neg_one_to_one(img)
+        return self.p_losses(img, t, *args, **kwargs)
+
+# dataset classes
+
+class Dataset(data.Dataset):
+    def __init__(self, folder, image_size, exts = ['jpg', 'jpeg', 'png']):
+        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([
+            transforms.Resize(image_size),
+            transforms.RandomHorizontalFlip(),
+            transforms.CenterCrop(image_size),
+            transforms.ToTensor()
+        ])
+
+    def __len__(self):
+        return len(self.paths)
+
+    def __getitem__(self, index):
+        path = self.paths[index]
+        img = Image.open(path)
+        return self.transform(img)
+
+# trainer class
+
+class Trainer(object):
+    def __init__(
+        self,
+        diffusion_model,
+        folder,
+        *,
+        ema_decay = 0.995,
+        image_size = 128,
+        train_batch_size = 32,
+        train_lr = 1e-4,
+        train_num_steps = 100000,
+        gradient_accumulate_every = 2,
+        amp = False,
+        step_start_ema = 2000,
+        update_ema_every = 10,
+        save_and_sample_every = 1000,
+        results_folder = './results'
+    ):
+        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.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)
+        self.dl = cycle(data.DataLoader(self.ds, batch_size = train_batch_size, shuffle=True, pin_memory=True))
+        self.opt = Adam(diffusion_model.parameters(), lr=train_lr)
+
+        self.step = 0
+
+        self.amp = amp
+        self.scaler = GradScaler(enabled = amp)
+
+        self.results_folder = Path(results_folder)
+        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):
+        data = {
+            'step': self.step,
+            'model': self.model.state_dict(),
+            'ema': self.ema_model.state_dict(),
+            'scaler': self.scaler.state_dict()
+        }
+        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'))
+
+        self.step = data['step']
+        self.model.load_state_dict(data['model'])
+        self.ema_model.load_state_dict(data['ema'])
+        self.scaler.load_state_dict(data['scaler'])
+
+    def train(self):
+        with tqdm(initial = self.step, total = self.train_num_steps) 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):
+                        loss = self.model(data)
+                        self.scaler.scale(loss / self.gradient_accumulate_every).backward()
+
+                    pbar.set_description(f'loss: {loss.item():.4f}')
+
+                self.scaler.step(self.opt)
+                self.scaler.update()
+                self.opt.zero_grad()
+
+                if self.step % self.update_ema_every == 0:
+                    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
+                pbar.update(1)
+
+        print('training complete')

denoising_diffusion_pytorch/learned_gaussian_diffusion.py

@@ -0,0 +1,132 @@
+import torch
+from math import pi, sqrt, log as ln
+from inspect import isfunction
+from torch import nn, einsum
+from einops import rearrange
+
+from denoising_diffusion_pytorch.denoising_diffusion_pytorch import GaussianDiffusion, extract, unnormalize_to_zero_to_one
+
+# constants
+
+NAT = 1. / ln(2)
+
+# helper functions
+
+def exists(x):
+    return x is not None
+
+def default(val, d):
+    if exists(val):
+        return val
+    return d() if isfunction(d) else d
+
+# tensor helpers
+
+def log(t, eps = 1e-12):
+    return torch.log(t.clamp(min = eps))
+
+def meanflat(x):
+    return x.mean(dim = tuple(range(1, len(x.shape))))
+
+def normal_kl(mean1, logvar1, mean2, logvar2):
+    """
+    KL divergence between normal distributions parameterized by mean and log-variance.
+    """
+    return 0.5 * (-1.0 + logvar2 - logvar1 + torch.exp(logvar1 - logvar2) + ((mean1 - mean2) ** 2) * torch.exp(-logvar2))
+
+def approx_standard_normal_cdf(x):
+    return 0.5 * (1.0 + torch.tanh(sqrt(2.0 / pi) * (x + 0.044715 * (x ** 3))))
+
+def discretized_gaussian_log_likelihood(x, *, means, log_scales, thres = 0.999):
+    assert x.shape == means.shape == log_scales.shape
+
+    centered_x = x - means
+    inv_stdv = torch.exp(-log_scales)
+    plus_in = inv_stdv * (centered_x + 1. / 255.)
+    cdf_plus = approx_standard_normal_cdf(plus_in)
+    min_in = inv_stdv * (centered_x - 1. / 255.)
+    cdf_min = approx_standard_normal_cdf(min_in)
+    log_cdf_plus = log(cdf_plus)
+    log_one_minus_cdf_min = log(1. - cdf_min)
+    cdf_delta = cdf_plus - cdf_min
+
+    log_probs = torch.where(x < -thres,
+        log_cdf_plus,
+        torch.where(x > thres,
+            log_one_minus_cdf_min,
+            log(cdf_delta)))
+
+    return log_probs
+
+# https://arxiv.org/abs/2102.09672
+
+# i thought the results were questionable, if one were to focus only on FID
+# but may as well get this in here for others to try, as GLIDE is using it (and DALL-E2 first stage of cascade)
+# gaussian diffusion for learned variance + hybrid eps simple + vb loss
+
+class LearnedGaussianDiffusion(GaussianDiffusion):
+    def __init__(
+        self,
+        denoise_fn,
+        vb_loss_weight = 0.001,  # lambda was 0.001 in the paper
+        *args,
+        **kwargs
+    ):
+        super().__init__(denoise_fn, *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`'
+        self.vb_loss_weight = vb_loss_weight
+
+    def p_mean_variance(self, *, x, t, clip_denoised, model_output = None):
+        model_output = default(model_output, lambda: self.denoise_fn(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)
+        max_log = extract(torch.log(self.betas), t, x.shape)
+        var_interp_frac = unnormalize_to_zero_to_one(var_interp_frac_unnormalized)
+
+        model_log_variance = var_interp_frac * max_log + (1 - var_interp_frac) * min_log
+        model_variance = model_log_variance.exp()
+
+        x_start = self.predict_start_from_noise(x, t, pred_noise)
+
+        if clip_denoised:
+            x_start.clamp_(-1., 1.)
+
+        model_mean, _, _ = self.q_posterior(x_start, x, t)
+
+        return model_mean, model_variance, model_log_variance
+
+    def p_losses(self, x_start, t, noise = None, clip_denoised = False):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+        x_t = self.q_sample(x_start = x_start, t = t, noise = noise)
+
+        # model output
+
+        model_output = self.denoise_fn(x_t, t)
+
+        # calculating kl loss for learned variance (interpolation)
+
+        true_mean, _, true_log_variance_clipped = self.q_posterior(x_start = x_start, x_t = x_t, t = t)
+        model_mean, _, model_log_variance = self.p_mean_variance(x = x_t, t = t, clip_denoised = clip_denoised, model_output = model_output)
+
+        # kl loss with detached model predicted mean, for stability reasons as in paper
+
+        detached_model_mean = model_mean.detach()
+
+        kl = normal_kl(true_mean, true_log_variance_clipped, detached_model_mean, model_log_variance)
+        kl = meanflat(kl) * NAT
+
+        decoder_nll = -discretized_gaussian_log_likelihood(x_start, means = detached_model_mean, log_scales = 0.5 * model_log_variance)
+        decoder_nll = meanflat(decoder_nll) * NAT
+
+        # at the first timestep return the decoder NLL, otherwise return KL(q(x_{t-1}|x_t,x_0) || p(x_{t-1}|x_t))
+
+        vb_losses = torch.where(t == 0, decoder_nll, kl)
+
+        # simple loss - predicting noise, x0, or x_prev
+
+        pred_noise, _ = model_output.chunk(2, dim = 1)
+
+        simple_losses = self.loss_fn(pred_noise, noise)
+
+        return simple_losses + vb_losses.mean() * self.vb_loss_weight

denoising_diffusion_pytorch/weighted_objective_gaussian_diffusion.py

@@ -0,0 +1,80 @@
+import torch
+from inspect import isfunction
+from torch import nn, einsum
+from einops import rearrange
+
+from denoising_diffusion_pytorch.denoising_diffusion_pytorch import GaussianDiffusion
+
+# helper functions
+
+def exists(x):
+    return x is not None
+
+def default(val, d):
+    if exists(val):
+        return val
+    return d() if isfunction(d) else d
+
+# some improvisation on my end
+# where i have the model learn to both predict noise and x0
+# and learn the weighted sum for each depending on time step
+
+class WeightedObjectiveGaussianDiffusion(GaussianDiffusion):
+    def __init__(
+        self,
+        denoise_fn,
+        *args,
+        pred_noise_loss_weight = 0.1,
+        pred_x_start_loss_weight = 0.1,
+        **kwargs
+    ):
+        super().__init__(denoise_fn, *args, **kwargs)
+        channels = denoise_fn.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'
+
+        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)
+
+        pred_noise, pred_x_start, weights = model_output.split(self.split_dims, dim = 1)
+        normalized_weights = weights.softmax(dim = 1)
+
+        x_start_from_noise = self.predict_start_from_noise(x, t = t, noise = pred_noise)
+        
+        x_starts = torch.stack((x_start_from_noise, pred_x_start), dim = 1)
+        weighted_x_start = einsum('b j h w, b j c h w -> b c h w', normalized_weights, x_starts)
+
+        if clip_denoised:
+            weighted_x_start.clamp_(-1., 1.)
+
+        model_mean, model_variance, model_log_variance = self.q_posterior(weighted_x_start, x, t)
+
+        return model_mean, model_variance, model_log_variance
+
+    def p_losses(self, x_start, t, noise = None, clip_denoised = False):
+        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)
+        pred_noise, pred_x_start, weights = model_output.split(self.split_dims, dim = 1)
+
+        # get loss for predicted noise and x_start
+        # with the loss weight given at initialization
+
+        noise_loss = self.loss_fn(noise, pred_noise) * self.pred_noise_loss_weight
+        x_start_loss = self.loss_fn(x_start, pred_x_start) * self.pred_x_start_loss_weight
+
+        # calculate x_start from predicted noise
+        # then do a weighted sum of the x_start prediction, weights also predicted by the model (softmax normalized)
+
+        x_start_from_pred_noise = self.predict_start_from_noise(x_t, t, pred_noise)
+        x_start_from_pred_noise = x_start_from_pred_noise.clamp(-2., 2.)
+        weighted_x_start = einsum('b j h w, b j c h w -> b c h w', weights.softmax(dim = 1), torch.stack((x_start_from_pred_noise, pred_x_start), dim = 1))
+
+        # main loss to x_start with the weighted one
+
+        weighted_x_start_loss = self.loss_fn(x_start, weighted_x_start)
+        return weighted_x_start_loss + x_start_loss + noise_loss

setup.py

@@ -3,7 +3,7 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.0.2',
+  version = '0.15.7',
   license='MIT',
   description = 'Denoising Diffusion Probabilistic Models - Pytorch',
   author = 'Phil Wang',
@@ -15,8 +15,9 @@ setup(
   ],
   install_requires=[
     'einops',
-    'numpy',
+    'pillow',
     'torch',
+    'torchvision',
     'tqdm'
   ],
   classifiers=[