get working version of gaussian diffusion with continuous time (only beta linear schedule for now, but will eventually contain alpha cosine schedule as well as parameterized, learned monotonic MLP)

README.md

@@ -34,7 +34,7 @@ diffusion = GaussianDiffusion(
     loss_type = 'l1'    # L1 or L2
 )
 
-training_images = torch.randn(8, 3, 128, 128) # your images need to be normalized from a range of -1 to +1
+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
@@ -64,7 +64,7 @@ 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
@@ -108,3 +108,14 @@ Samples and model checkpoints will be logged to `./results` periodically
     url         = {https://proceedings.mlr.press/v139/nichol21a.html},
 }
 ```
+
+```bibtex
+@inproceedings{kingma2021on,
+    title       = {On Density Estimation with Diffusion Models},
+    author      = {Diederik P Kingma and Tim Salimans and Ben Poole and Jonathan Ho},
+    booktitle   = {Advances in Neural Information Processing Systems},
+    editor      = {A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
+    year        = {2021},
+    url         = {https://openreview.net/forum?id=2LdBqxc1Yv}
+}
+```

denoising_diffusion_pytorch/__init__.py

@@ -1,2 +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 +1,187 @@
+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)
+        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

@@ -118,20 +118,27 @@ class PreNorm(nn.Module):
 class Block(nn.Module):
     def __init__(self, dim, dim_out, groups = 8):
         super().__init__()
-        self.block = nn.Sequential(
+        self.proj = nn.Conv2d(dim, dim_out, 3, padding = 1)
-            nn.Conv2d(dim, dim_out, 3, padding = 1),
+        self.norm = nn.GroupNorm(groups, dim_out)
-            nn.GroupNorm(groups, dim_out),
+        self.act = nn.SiLU()
-            nn.SiLU()
+
-        )
+    def forward(self, x, scale_shift = None):
-    def forward(self, x):
+        x = self.proj(x)
-        return self.block(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)
+            nn.Linear(time_emb_dim, dim_out * 2)
         ) if exists(time_emb_dim) else None
 
         self.block1 = Block(dim, dim_out, groups = groups)
@@ -139,11 +146,14 @@ class ResnetBlock(nn.Module):
         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.block1(x)
 
+        scale_shift = 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
+            time_emb = rearrange(time_emb, 'b c -> b c 1 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)
@@ -314,10 +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):
     """
@@ -339,7 +350,9 @@ class GaussianDiffusion(nn.Module):
         image_size,
         channels = 3,
         timesteps = 1000,
-        loss_type = 'l1'
+        loss_type = 'l1',
+        objective = 'pred_noise',
+        beta_schedule = 'cosine'
     ):
         super().__init__()
         assert not (type(self) == GaussianDiffusion and denoise_fn.channels != denoise_fn.out_dim)
@@ -347,8 +360,14 @@ class GaussianDiffusion(nn.Module):
         self.channels = channels
         self.image_size = image_size
         self.denoise_fn = denoise_fn
+        self.objective = objective
 
-        betas = cosine_beta_schedule(timesteps)
+        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, axis=0)
@@ -388,12 +407,6 @@ class GaussianDiffusion(nn.Module):
         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 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
-
     def predict_start_from_noise(self, x_t, t, noise):
         return (
             extract(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t -
@@ -410,19 +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
@@ -436,6 +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()
@@ -481,17 +503,26 @@ class GaussianDiffusion(nn.Module):
         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)
 
-        loss = self.loss_fn(noise, x_recon)
+        if self.objective == 'pred_noise':
+            target = noise
+        elif self.objective == 'pred_x0':
+            target = x_start
+        else:
+            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
 
@@ -506,8 +537,7 @@ class Dataset(data.Dataset):
             transforms.Resize(image_size),
             transforms.RandomHorizontalFlip(),
             transforms.CenterCrop(image_size),
-            transforms.ToTensor(),
+            transforms.ToTensor()
-            transforms.Lambda(normalize_to_neg_one_to_one)
         ])
 
     def __len__(self):
@@ -529,7 +559,7 @@ 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,
         amp = False,
@@ -593,34 +623,36 @@ class Trainer(object):
         self.scaler.load_state_dict(data['scaler'])
 
     def train(self):
-        while self.step < self.train_num_steps:
+        with tqdm(initial = self.step, total = self.train_num_steps) as pbar:
-            for i in range(self.gradient_accumulate_every):
-                data = next(self.dl).cuda()
 
-                with autocast(enabled = self.amp):
+            while self.step < self.train_num_steps:
-                    loss = self.model(data)
+                for i in range(self.gradient_accumulate_every):
-                    self.scaler.scale(loss / self.gradient_accumulate_every).backward()
+                    data = next(self.dl).cuda()
 
-                print(f'{self.step}: {loss.item()}')
+                    with autocast(enabled = self.amp):
+                        loss = self.model(data)
+                        self.scaler.scale(loss / self.gradient_accumulate_every).backward()
 
-            self.scaler.step(self.opt)
+                    pbar.set_description(f'loss: {loss.item():.4f}')
-            self.scaler.update()
-            self.opt.zero_grad()
 
-            if self.step % self.update_ema_every == 0:
+                self.scaler.step(self.opt)
-                self.step_ema()
+                self.scaler.update()
+                self.opt.zero_grad()
 
-            if self.step != 0 and self.step % self.save_and_sample_every == 0:
+                if self.step % self.update_ema_every == 0:
-                self.ema_model.eval()
+                    self.step_ema()
 
-                milestone = self.step // self.save_and_sample_every
+                if self.step != 0 and self.step % self.save_and_sample_every == 0:
-                batches = num_to_groups(36, self.batch_size)
+                    self.ema_model.eval()
-                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 = unnormalize_to_zero_to_one(all_images)
-                utils.save_image(all_images, str(self.results_folder / f'sample-{milestone}.png'), nrow = 6)
-                self.save(milestone)
 
-            self.step += 1
+                    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)
 
-        print('training completed')
+                self.step += 1
+                pbar.update(1)
+
+        print('training complete')

denoising_diffusion_pytorch/learned_gaussian_diffusion.py

@@ -76,25 +76,6 @@ class LearnedGaussianDiffusion(GaussianDiffusion):
         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 q_posterior_mean_variance(self, x_start, x_t, t):
-        """
-        Compute the mean and variance of the diffusion posterior q(x_{t-1} | x_t, x_0)
-        """
-        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 predict_xstart_from_xprev(self, x_t, t, xprev):
-        # (xprev - coef2*x_t) / coef1
-        return (
-            extract(1. / self.posterior_mean_coef1, t, x_t.shape) * xprev -
-            extract(self.posterior_mean_coef2 / self.posterior_mean_coef1, t, x_t.shape) * x_t
-        )
-
     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)
@@ -125,7 +106,7 @@ class LearnedGaussianDiffusion(GaussianDiffusion):
 
         # calculating kl loss for learned variance (interpolation)
 
-        true_mean, _, true_log_variance_clipped = self.q_posterior_mean_variance(x_start = x_start, x_t = x_t, t = t)
+        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

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

@@ -3,12 +3,13 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.14.2',
+  version = '0.16.3',
   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'