alpha cosine noise schedule is now working for continuous time gaussian diffusion

README.md

@@ -6,6 +6,8 @@ Implementation of <a href="https://arxiv.org/abs/2006.11239">Denoising Diffusion
 
 This implementation was transcribed from the official Tensorflow version <a href="https://github.com/hojonathanho/diffusion">here</a>
 
+<a href="https://huggingface.co/blog/annotated-diffusion">Annotated code</a> by Research Scientists / Engineers from <a href="https://huggingface.co/">🤗 Huggingface</a>
+
 <img src="./sample.png" width="500px"><img>
 
 [![PyPI version](https://badge.fury.io/py/denoising-diffusion-pytorch.svg)](https://badge.fury.io/py/denoising-diffusion-pytorch)

denoising_diffusion_pytorch/continuous_time_gaussian_diffusion.py

@@ -6,6 +6,7 @@ from torch.special import expm1
 
 from tqdm import tqdm
 from einops import rearrange, repeat
+from einops.layers.torch import Rearrange
 
 # helpers
 
@@ -33,6 +34,24 @@ def right_pad_dims_to(x, t):
         return t
     return t.view(*t.shape, *((1,) * padding_dims))
 
+# neural net helpers
+
+class Residual(nn.Module):
+    def __init__(self, fn):
+        super().__init__()
+        self.fn = fn
+
+    def forward(self, x):
+        return x + self.fn(x)
+
+class MonotonicLinear(nn.Module):
+    def __init__(self, *args, **kwargs):
+        super().__init__()
+        self.net = nn.Linear(*args, **kwargs)
+
+    def forward(self, x):
+        return F.linear(x, self.net.weight.abs(), self.net.bias.abs())
+
 # continuous schedules
 
 # equations are taken from https://openreview.net/attachment?id=2LdBqxc1Yv&name=supplementary_material
@@ -40,17 +59,54 @@ def right_pad_dims_to(x, t):
 
 # log(snr) that approximates the original linear schedule
 
-def beta_linear_log_snr(t):
+def log(t, eps = 1e-20):
-    return -torch.log(expm1(1e-4 + 10 * (t ** 2)))
+    return torch.log(t.clamp(min = eps))
 
-def alpha_cosine_log_snr(t):
+def beta_linear_log_snr(t):
-    raise NotImplementedError
+    return -log(expm1(1e-4 + 10 * (t ** 2)))
+
+def alpha_cosine_log_snr(t, s = 0.008):
+    return -log((torch.cos((t + s) / (1 + s) * torch.pi * 0.5) ** -2) - 1)
 
 class learned_noise_schedule(nn.Module):
-    def __init__(self):
+    """ described in section H and then I.2 of the supplementary material for variational ddpm paper """
+
+    def __init__(
+        self,
+        *,
+        log_snr_max,
+        log_snr_min,
+        hidden_dim = 1024,
+        frac_gradient = 1.
+    ):
         super().__init__()
-        raise NotImplementedError
+        self.slope = log_snr_min - log_snr_max
-        # learned noise schedule, using learned monotonic MLP (weights kept positive) in the paper
+        self.intercept = log_snr_max
+
+        self.net = nn.Sequential(
+            Rearrange('... -> ... 1'),
+            MonotonicLinear(1, 1),
+            Residual(nn.Sequential(
+                MonotonicLinear(1, hidden_dim),
+                nn.Sigmoid(),
+                MonotonicLinear(hidden_dim, 1)
+            )),
+            Rearrange('... 1 -> ...'),
+        )
+
+        self.frac_gradient = frac_gradient
+
+    def forward(self, x):
+        frac_gradient = self.frac_gradient
+        device = x.device
+
+        out_zero = self.net(torch.zeros_like(x))
+        out_one =  self.net(torch.ones_like(x))
+
+        x = self.net(x)
+
+        normed = self.slope * ((x - out_zero) / (out_one - out_zero)) + self.intercept
+        return normed * frac_gradient + normed.detach() * (1 - frac_gradient)
 
 class ContinuousTimeGaussianDiffusion(nn.Module):
     def __init__(
@@ -61,7 +117,10 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         channels = 3,
         loss_type = 'l1',
         noise_schedule = 'linear',
-        num_sample_steps = 500
+        num_sample_steps = 500,
+        clip_sample_denoised = True,
+        learned_schedule_net_hidden_dim = 1024,
+        learned_noise_schedule_frac_gradient = 1.   # between 0 and 1, determines what percentage of gradients go back, so one can update the learned noise schedule more slowly
     ):
         super().__init__()
         assert not denoise_fn.sinusoidal_cond_mlp
@@ -79,12 +138,24 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
 
         if noise_schedule == 'linear':
             self.log_snr = beta_linear_log_snr
+        elif noise_schedule == 'cosine':
+            self.log_snr = alpha_cosine_log_snr
+        elif noise_schedule == 'learned':
+            log_snr_max, log_snr_min = [beta_linear_log_snr(torch.tensor([time])).item() for time in (0., 1.)]
+
+            self.log_snr = learned_noise_schedule(
+                log_snr_max = log_snr_max,
+                log_snr_min = log_snr_min,
+                hidden_dim = learned_schedule_net_hidden_dim,
+                frac_gradient = learned_noise_schedule_frac_gradient
+            )
         else:
             raise ValueError(f'unknown noise schedule {noise_schedule}')
 
         # sampling
 
         self.num_sample_steps = num_sample_steps
+        self.clip_sample_denoised = clip_sample_denoised
 
     @property
     def device(self):
@@ -103,9 +174,6 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         # 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
-
         log_snr = self.log_snr(time)
         log_snr_next = self.log_snr(time_next)
         c = -expm1(log_snr - log_snr_next)
@@ -113,10 +181,21 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         squared_alpha, squared_alpha_next = log_snr.sigmoid(), log_snr_next.sigmoid()
         squared_sigma, squared_sigma_next = (-log_snr).sigmoid(), (-log_snr_next).sigmoid()
 
+        alpha, sigma, alpha_next = map(sqrt, (squared_alpha, squared_sigma, squared_alpha_next))
+
         batch_log_snr = repeat(log_snr, ' -> b', b = x.shape[0])
         pred_noise = self.denoise_fn(x, batch_log_snr)
 
-        model_mean = sqrt(squared_alpha_next / squared_alpha) * (x - c * sqrt(squared_sigma) * pred_noise)
+        if self.clip_sample_denoised:
+            x_start = (x - sigma * pred_noise) / alpha
+
+            # in Imagen, this was changed to dynamic thresholding
+            x_start.clamp_(-1., 1.)
+
+            model_mean = alpha_next * (x * (1 - c) / alpha + c * x_start)
+        else:
+            model_mean = alpha_next / alpha * (x - c * sigma * pred_noise)
+
         posterior_variance = squared_sigma_next * c
 
         return model_mean, posterior_variance

setup.py

@@ -3,7 +3,7 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.16.7',
+  version = '0.17.7',
   license='MIT',
   description = 'Denoising Diffusion Probabilistic Models - Pytorch',
   author = 'Phil Wang',