assume when sampling all batch samples are at the same time, and do not noise for the last time step

updated citation in README

README.md

@@ -4,7 +4,7 @@
 
 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> and then modified to use <a href="https://arxiv.org/abs/2201.03545">ConvNext</a> blocks instead of Resnets.
+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>
 
@@ -34,7 +34,7 @@ diffusion = GaussianDiffusion(
     loss_type = 'l1'    # L1 or L2
 )
 
-training_images = torch.randn(8, 3, 128, 128)
+training_images = torch.randn(8, 3, 128, 128) # images are normalized from 0 to 1
 loss = diffusion(training_images)
 loss.backward()
 # after a lot of training
@@ -64,11 +64,11 @@ trainer = Trainer(
     diffusion,
     'path/to/your/images',
     train_batch_size = 32,
-    train_lr = 2e-5,
+    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
-    fp16 = True                       # turn on mixed precision training with apex
+    amp = True                        # turn on mixed precision
 )
 
 trainer.train()
@@ -79,34 +79,43 @@ Samples and model checkpoints will be logged to `./results` periodically
 ## Citations
 
 ```bibtex
-@misc{ho2020denoising,
+@inproceedings{NEURIPS2020_4c5bcfec,
-    title   = {Denoising Diffusion Probabilistic Models},
+    author      = {Ho, Jonathan and Jain, Ajay and Abbeel, Pieter},
-    author  = {Jonathan Ho and Ajay Jain and Pieter Abbeel},
+    booktitle   = {Advances in Neural Information Processing Systems},
-    year    = {2020},
+    editor      = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
-    eprint  = {2006.11239},
+    pages       = {6840--6851},
-    archivePrefix = {arXiv},
+    publisher   = {Curran Associates, Inc.},
-    primaryClass = {cs.LG}
+    title       = {Denoising Diffusion Probabilistic Models},
+    url         = {https://proceedings.neurips.cc/paper/2020/file/4c5bcfec8584af0d967f1ab10179ca4b-Paper.pdf},
+    volume      = {33},
+    year        = {2020}
 }
 ```
 
 ```bibtex
-@inproceedings{anonymous2021improved,
+@InProceedings{pmlr-v139-nichol21a,
-    title   = {Improved Denoising Diffusion Probabilistic Models},
+    title       = {Improved Denoising Diffusion Probabilistic Models},
-    author  = {Anonymous},
+    author      = {Nichol, Alexander Quinn and Dhariwal, Prafulla},
-    booktitle = {Submitted to International Conference on Learning Representations},
+    booktitle   = {Proceedings of the 38th International Conference on Machine Learning},
-    year    = {2021},
+    pages       = {8162--8171},
-    url     = {https://openreview.net/forum?id=-NEXDKk8gZ},
+    year        = {2021},
-    note    = {under review}
+    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},
 }
 ```
 
 ```bibtex
-@misc{liu2022convnet,
+@inproceedings{kingma2021on,
-    title   = {A ConvNet for the 2020s},
+    title       = {On Density Estimation with Diffusion Models},
-    author  = {Zhuang Liu and Hanzi Mao and Chao-Yuan Wu and Christoph Feichtenhofer and Trevor Darrell and Saining Xie},
+    author      = {Diederik P Kingma and Tim Salimans and Ben Poole and Jonathan Ho},
-    year    = {2022},
+    booktitle   = {Advances in Neural Information Processing Systems},
-    eprint  = {2201.03545},
+    editor      = {A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
-    archivePrefix = {arXiv},
+    year        = {2021},
-    primaryClass = {cs.CV}
+    url         = {https://openreview.net/forum?id=2LdBqxc1Yv}
 }
 ```

denoising_diffusion_pytorch/__init__.py

@@ -1 +1,5 @@
 from denoising_diffusion_pytorch.denoising_diffusion_pytorch import GaussianDiffusion, Unet, Trainer
+
+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

denoising_diffusion_pytorch/continuous_time_gaussian_diffusion.py

@@ -0,0 +1,191 @@
+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
+
+# 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
+
+# equations are taken from https://openreview.net/attachment?id=2LdBqxc1Yv&name=supplementary_material
+# @crowsonkb Katherine's repository also helped here https://github.com/crowsonkb/v-diffusion-jax/blob/master/diffusion/utils.py
+
+# log(snr) that approximates the original linear schedule
+
+def beta_linear_log_snr(t):
+    return -torch.log(expm1(1e-4 + 10 * (t ** 2)))
+
+def alpha_cosine_log_snr(t):
+    raise NotImplementedError
+
+class learned_noise_schedule(nn.Module):
+    def __init__(self):
+        super().__init__()
+        raise NotImplementedError
+        # learned noise schedule, using learned monotonic MLP (weights kept positive) in the paper
+
+class ContinuousTimeGaussianDiffusion(nn.Module):
+    def __init__(
+        self,
+        denoise_fn,
+        *,
+        image_size,
+        channels = 3,
+        cond_scale = 500,
+        loss_type = 'l1',
+        noise_schedule = 'linear',
+        num_sample_steps = 500
+    ):
+        super().__init__()
+
+        self.denoise_fn = denoise_fn
+
+        # image dimensions
+
+        self.channels = channels
+        self.image_size = image_size
+
+        # continuous noise schedule related stuff
+
+        self.cond_scale = cond_scale # the log(snr) will be scaled by this value
+        self.loss_type = loss_type
+
+        if noise_schedule == 'linear':
+            self.log_snr = beta_linear_log_snr
+        else:
+            raise ValueError(f'unknown noise schedule {noise_schedule}')
+
+        # sampling
+
+        self.num_sample_steps = num_sample_steps
+
+    @property
+    def device(self):
+        return next(self.denoise_fn.parameters()).device
+
+    @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_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
+
+        # todo - derive x_start from the posterior mean and do dynamic thresholding
+        # assumed that is what is going on in Imagen
+
+        batch = x.shape[0]
+        batch_time = repeat(time, ' -> b', b = batch)
+
+        pred_noise = self.denoise_fn(x, batch_time * self.cond_scale)
+
+        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()
+
+        model_mean = sqrt(squared_alpha_next / squared_alpha) * (x - c * sqrt(squared_sigma) * pred_noise)
+        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 = 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
+
+    def random_times(self, batch_size):
+        # times are now uniform from 0 to 1
+        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 = self.q_sample(x_start = x_start, times = times, noise = noise)
+
+        model_out = self.denoise_fn(x, log_snr * self.cond_scale)
+        return self.loss_fn(model_out, noise)
+
+    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/denoising_diffusion_pytorch.py

@@ -7,21 +7,16 @@ 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
 
-try:
-    from apex import amp
-    APEX_AVAILABLE = True
-except:
-    APEX_AVAILABLE = False
-
 # helpers functions
 
 def exists(x):
@@ -45,12 +40,11 @@ def num_to_groups(num, divisor):
         arr.append(remainder)
     return arr
 
-def loss_backwards(fp16, loss, optimizer, **kwargs):
+def normalize_to_neg_one_to_one(img):
-    if fp16:
+    return img * 2 - 1
-        with amp.scale_loss(loss, optimizer) as scaled_loss:
+
-            scaled_loss.backward(**kwargs)
+def unnormalize_to_zero_to_one(t):
-    else:
+    return (t + 1) * 0.5
-        loss.backward(**kwargs)
 
 # small helper modules
 
@@ -121,36 +115,47 @@ class PreNorm(nn.Module):
 
 # building block modules
 
-class ConvNextBlock(nn.Module):
+class Block(nn.Module):
-    """ https://arxiv.org/abs/2201.03545 """
+    def __init__(self, dim, dim_out, groups = 8):
+        super().__init__()
+        self.proj = nn.Conv2d(dim, dim_out, 3, padding = 1)
+        self.norm = nn.GroupNorm(groups, dim_out)
+        self.act = nn.SiLU()
 
-    def __init__(self, dim, dim_out, *, time_emb_dim = None, mult = 2, norm = True):
+    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.GELU(),
+            nn.SiLU(),
-            nn.Linear(time_emb_dim, dim)
+            nn.Linear(time_emb_dim, dim_out * 2)
         ) if exists(time_emb_dim) else None
 
-        self.ds_conv = nn.Conv2d(dim, dim, 7, padding = 3, groups = dim)
+        self.block1 = Block(dim, dim_out, groups = groups)
-
+        self.block2 = Block(dim_out, dim_out, groups = groups)
-        self.net = nn.Sequential(
-            LayerNorm(dim) if norm else nn.Identity(),
-            nn.Conv2d(dim, dim_out * mult, 3, padding = 1),
-            nn.GELU(),
-            nn.Conv2d(dim_out * mult, dim_out, 3, padding = 1)
-        )
-
         self.res_conv = nn.Conv2d(dim, dim_out, 1) if dim != dim_out else nn.Identity()
 
     def forward(self, x, time_emb = None):
-        h = self.ds_conv(x)
 
-        if exists(self.mlp):
+        scale_shift = None
-            assert exists(time_emb), 'time emb must be passed in'
+        if exists(self.mlp) and exists(time_emb):
-            condition = self.mlp(time_emb)
+            time_emb = self.mlp(time_emb)
-            h = h + rearrange(condition, 'b c -> b c 1 1')
+            time_emb = rearrange(time_emb, 'b c -> b c 1 1')
+            scale_shift = time_emb.chunk(2, dim = 1)
 
-        h = self.net(h)
+        h = self.block1(x, scale_shift = scale_shift)
+
+        h = self.block2(h)
         return h + self.res_conv(x)
 
 class LinearAttention(nn.Module):
@@ -160,15 +165,21 @@ class LinearAttention(nn.Module):
         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)
+
+        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 * self.scale
 
+        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)
@@ -204,29 +215,44 @@ class Unet(nn.Module):
     def __init__(
         self,
         dim,
+        init_dim = None,
         out_dim = None,
         dim_mults=(1, 2, 4, 8),
         channels = 3,
-        with_time_emb = True
+        with_time_emb = True,
+        resnet_block_groups = 8,
+        learned_variance = False
     ):
         super().__init__()
+
+        # determine dimensions
+
         self.channels = channels
 
-        dims = [channels, *map(lambda m: dim * m, dim_mults)]
+        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:]))
 
+        block_klass = partial(ResnetBlock, groups = resnet_block_groups)
+
+        # time embeddings
+
         if with_time_emb:
-            time_dim = dim
+            time_dim = dim * 4
             self.time_mlp = nn.Sequential(
                 SinusoidalPosEmb(dim),
-                nn.Linear(dim, dim * 4),
+                nn.Linear(dim, time_dim),
                 nn.GELU(),
-                nn.Linear(dim * 4, dim)
+                nn.Linear(time_dim, time_dim)
             )
         else:
             time_dim = None
             self.time_mlp = None
 
+        # layers
+
         self.downs = nn.ModuleList([])
         self.ups = nn.ModuleList([])
         num_resolutions = len(in_out)
@@ -235,41 +261,45 @@ class Unet(nn.Module):
             is_last = ind >= (num_resolutions - 1)
 
             self.downs.append(nn.ModuleList([
-                ConvNextBlock(dim_in, dim_out, time_emb_dim = time_dim, norm = ind != 0),
+                block_klass(dim_in, dim_out, time_emb_dim = time_dim),
-                ConvNextBlock(dim_out, 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 = ConvNextBlock(mid_dim, mid_dim, time_emb_dim = time_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 = ConvNextBlock(mid_dim, mid_dim, time_emb_dim = time_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([
-                ConvNextBlock(dim_out * 2, dim_in, time_emb_dim = time_dim),
+                block_klass(dim_out * 2, dim_in, time_emb_dim = time_dim),
-                ConvNextBlock(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))),
                 Upsample(dim_in) if not is_last else nn.Identity()
             ]))
 
-        out_dim = default(out_dim, channels)
+        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(
-            ConvNextBlock(dim, dim),
+            block_klass(dim, dim),
-            nn.Conv2d(dim, out_dim, 1)
+            nn.Conv2d(dim, self.out_dim, 1)
         )
 
     def forward(self, x, time):
+        x = self.init_conv(x)
+
         t = self.time_mlp(time) if exists(self.time_mlp) else None
 
         h = []
 
-        for convnext, convnext2, attn, downsample in self.downs:
+        for block1, block2, attn, downsample in self.downs:
-            x = convnext(x, t)
+            x = block1(x, t)
-            x = convnext2(x, t)
+            x = block2(x, t)
             x = attn(x)
             h.append(x)
             x = downsample(x)
@@ -278,10 +308,10 @@ class Unet(nn.Module):
         x = self.mid_attn(x)
         x = self.mid_block2(x, t)
 
-        for convnext, convnext2, attn, upsample in self.ups:
+        for block1, block2, attn, upsample in self.ups:
             x = torch.cat((x, h.pop()), dim=1)
-            x = convnext(x, t)
+            x = block1(x, t)
-            x = convnext2(x, t)
+            x = block2(x, t)
             x = attn(x)
             x = upsample(x)
 
@@ -294,10 +324,11 @@ def extract(a, t, x_shape):
     out = a.gather(-1, t)
     return out.reshape(b, *((1,) * (len(x_shape) - 1)))
 
-def noise_like(shape, device, repeat=False):
+def linear_beta_schedule(timesteps):
-    repeat_noise = lambda: torch.randn((1, *shape[1:]), device=device).repeat(shape[0], *((1,) * (len(shape) - 1)))
+    scale = 1000 / timesteps
-    noise = lambda: torch.randn(shape, device=device)
+    beta_start = scale * 0.0001
-    return repeat_noise() if repeat else noise()
+    beta_end = scale * 0.02
+    return torch.linspace(beta_start, beta_end, timesteps, dtype = torch.float64)
 
 def cosine_beta_schedule(timesteps, s = 0.008):
     """
@@ -305,11 +336,11 @@ def cosine_beta_schedule(timesteps, s = 0.008):
     as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
     """
     steps = timesteps + 1
-    x = np.linspace(0, steps, steps)
+    x = torch.linspace(0, timesteps, steps, dtype = torch.float64)
-    alphas_cumprod = np.cos(((x / steps) + s) / (1 + s) * np.pi * 0.5) ** 2
+    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 np.clip(betas, a_min = 0, a_max = 0.999)
+    return torch.clip(betas, 0, 0.999)
 
 class GaussianDiffusion(nn.Module):
     def __init__(
@@ -320,55 +351,61 @@ class GaussianDiffusion(nn.Module):
         channels = 3,
         timesteps = 1000,
         loss_type = 'l1',
-        betas = None
+        objective = 'pred_noise',
+        beta_schedule = 'cosine'
     ):
         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
 
-        if exists(betas):
+        if beta_schedule == 'linear':
-            betas = betas.detach().cpu().numpy() if isinstance(betas, torch.Tensor) else betas
+            betas = linear_beta_schedule(timesteps)
-        else:
+        elif beta_schedule == 'cosine':
             betas = cosine_beta_schedule(timesteps)
+        else:
+            raise ValueError(f'unknown beta schedule {beta_schedule}')
 
         alphas = 1. - betas
-        alphas_cumprod = np.cumprod(alphas, axis=0)
+        alphas_cumprod = torch.cumprod(alphas, axis=0)
-        alphas_cumprod_prev = np.append(1., alphas_cumprod[:-1])
+        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
 
-        to_torch = partial(torch.tensor, dtype=torch.float32)
+        # helper function to register buffer from float64 to float32
 
-        self.register_buffer('betas', to_torch(betas))
+        register_buffer = lambda name, val: self.register_buffer(name, val.to(torch.float32))
-        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)))
+        register_buffer('sqrt_alphas_cumprod', torch.sqrt(alphas_cumprod))
-        self.register_buffer('log_one_minus_alphas_cumprod', to_torch(np.log(1. - alphas_cumprod)))
+        register_buffer('sqrt_one_minus_alphas_cumprod', torch.sqrt(1. - alphas_cumprod))
-        self.register_buffer('sqrt_recip_alphas_cumprod', to_torch(np.sqrt(1. / alphas_cumprod)))
+        register_buffer('log_one_minus_alphas_cumprod', torch.log(1. - alphas_cumprod))
-        self.register_buffer('sqrt_recipm1_alphas_cumprod', to_torch(np.sqrt(1. / alphas_cumprod - 1)))
+        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):
+        posterior_variance = betas * (1. - alphas_cumprod_prev) / (1. - alphas_cumprod)
-        mean = extract(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
+
-        variance = extract(1. - self.alphas_cumprod, t, x_start.shape)
+        # above: equal to 1. / (1. / (1. - alpha_cumprod_tm1) + alpha_t / beta_t)
-        log_variance = extract(self.log_one_minus_alphas_cumprod, t, x_start.shape)
+
-        return mean, variance, log_variance
+        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 (
@@ -386,19 +423,26 @@ 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()
-    def p_sample(self, x, t, clip_denoised=True, repeat_noise=False):
+    def p_sample(self, x, t, 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)
-        noise = noise_like(x.shape, device, repeat_noise)
+        noise = torch.randn_like(x)
         # no noise when t == 0
         nonzero_mask = (1 - (t == 0).float()).reshape(b, *((1,) * (len(x.shape) - 1)))
         return model_mean + nonzero_mask * (0.5 * model_log_variance).exp() * noise
@@ -412,6 +456,8 @@ 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()
@@ -444,27 +490,39 @@ 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 = self.q_sample(x_start=x_start, t=t, noise=noise)
-        x_recon = self.denoise_fn(x_noisy, t)
+        model_out = self.denoise_fn(x, t)
 
-        if self.loss_type == 'l1':
+        if self.objective == 'pred_noise':
-            loss = (noise - x_recon).abs().mean()
+            target = noise
-        elif self.loss_type == 'l2':
+        elif self.objective == 'pred_x0':
-            loss = F.mse_loss(noise, x_recon)
+            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):
+    def forward(self, img, *args, **kwargs):
-        b, c, h, w, device, img_size, = *x.shape, x.device, self.image_size
+        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
 
@@ -479,8 +537,7 @@ class Dataset(data.Dataset):
             transforms.Resize(image_size),
             transforms.RandomHorizontalFlip(),
             transforms.CenterCrop(image_size),
-            transforms.ToTensor(),
+            transforms.ToTensor()
-            transforms.Lambda(lambda t: (t * 2) - 1)
         ])
 
     def __len__(self):
@@ -502,10 +559,10 @@ class Trainer(object):
         ema_decay = 0.995,
         image_size = 128,
         train_batch_size = 32,
-        train_lr = 2e-5,
+        train_lr = 1e-4,
         train_num_steps = 100000,
         gradient_accumulate_every = 2,
-        fp16 = False,
+        amp = False,
         step_start_ema = 2000,
         update_ema_every = 10,
         save_and_sample_every = 1000,
@@ -531,11 +588,8 @@ class Trainer(object):
 
         self.step = 0
 
-        assert not fp16 or fp16 and APEX_AVAILABLE, 'Apex must be installed in order for mixed precision training to be turned on'
+        self.amp = amp
-
+        self.scaler = GradScaler(enabled = amp)
-        self.fp16 = fp16
-        if fp16:
-            (self.model, self.ema_model), self.opt = amp.initialize([self.model, self.ema_model], self.opt, opt_level='O1')
 
         self.results_folder = Path(results_folder)
         self.results_folder.mkdir(exist_ok = True)
@@ -555,7 +609,8 @@ class Trainer(object):
         data = {
             'step': self.step,
             'model': self.model.state_dict(),
-            'ema': self.ema_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'))
 
@@ -565,32 +620,39 @@ class Trainer(object):
         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):
-        backwards = partial(loss_backwards, self.fp16)
+        with tqdm(initial = self.step, total = self.train_num_steps) as pbar:
 
-        while self.step < self.train_num_steps:
+            while self.step < self.train_num_steps:
-            for i in range(self.gradient_accumulate_every):
+                for i in range(self.gradient_accumulate_every):
-                data = next(self.dl).cuda()
+                    data = next(self.dl).cuda()
-                loss = self.model(data)
-                print(f'{self.step}: {loss.item()}')
-                backwards(loss / self.gradient_accumulate_every, self.opt)
 
-            self.opt.step()
+                    with autocast(enabled = self.amp):
-            self.opt.zero_grad()
+                        loss = self.model(data)
+                        self.scaler.scale(loss / self.gradient_accumulate_every).backward()
 
-            if self.step % self.update_ema_every == 0:
+                    pbar.set_description(f'loss: {loss.item():.4f}')
-                self.step_ema()
 
-            if self.step != 0 and self.step % self.save_and_sample_every == 0:
+                self.scaler.step(self.opt)
-                milestone = self.step // self.save_and_sample_every
+                self.scaler.update()
-                batches = num_to_groups(36, self.batch_size)
+                self.opt.zero_grad()
-                all_images_list = list(map(lambda n: self.ema_model.sample(batch_size=n), batches))
-                all_images = torch.cat(all_images_list, dim=0)
-                all_images = (all_images + 1) * 0.5
-                utils.save_image(all_images, str(self.results_folder / f'sample-{milestone}.png'), nrow = 6)
-                self.save(milestone)
 
-            self.step += 1
+                if self.step % self.update_ema_every == 0:
+                    self.step_ema()
 
-        print('training completed')
+                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

@@ -3,19 +3,19 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.8.0',
+  version = '0.16.4',
   license='MIT',
   description = 'Denoising Diffusion Probabilistic Models - Pytorch',
   author = 'Phil Wang',
   author_email = 'lucidrains@gmail.com',
   url = 'https://github.com/lucidrains/denoising-diffusion-pytorch',
+  long_description_content_type = 'text/markdown',
   keywords = [
     'artificial intelligence',
     'generative models'
   ],
   install_requires=[
     'einops',
-    'numpy',
     'pillow',
     'torch',
     'torchvision',