add the v-parameterization from Salimans et al for the discrete case, allow for distillation

README.md

@@ -195,3 +195,13 @@ $ accelerate launch train.py
     volume  = {abs/1903.10520}
 }
 ```
+
+```bibtex
+@article{Salimans2022ProgressiveDF,
+    title   = {Progressive Distillation for Fast Sampling of Diffusion Models},
+    author  = {Tim Salimans and Jonathan Ho},
+    journal = {ArXiv},
+    year    = {2022},
+    volume  = {abs/2202.00512}
+}
+```

denoising_diffusion_pytorch/__init__.py

@@ -4,3 +4,4 @@ from denoising_diffusion_pytorch.learned_gaussian_diffusion import LearnedGaussi
 from denoising_diffusion_pytorch.continuous_time_gaussian_diffusion import ContinuousTimeGaussianDiffusion
 from denoising_diffusion_pytorch.weighted_objective_gaussian_diffusion import WeightedObjectiveGaussianDiffusion
 from denoising_diffusion_pytorch.elucidated_diffusion import ElucidatedDiffusion
+from denoising_diffusion_pytorch.v_param_continuous_time_gaussian_diffusion import VParamContinuousTimeGaussianDiffusion

denoising_diffusion_pytorch/continuous_time_gaussian_diffusion.py

@@ -126,7 +126,7 @@ class ContinuousTimeGaussianDiffusion(nn.Module):
         p2_loss_weight_k = 1
     ):
         super().__init__()
-        assert model.learned_sinusoidal_cond
+        assert model.random_or_learned_sinusoidal_cond
         assert not model.self_condition, 'not supported yet'
 
         self.model = model

denoising_diffusion_pytorch/denoising_diffusion_pytorch.py

@@ -140,15 +140,15 @@ class SinusoidalPosEmb(nn.Module):
         emb = torch.cat((emb.sin(), emb.cos()), dim=-1)
         return emb
 
-class LearnedSinusoidalPosEmb(nn.Module):
+class RandomOrLearnedSinusoidalPosEmb(nn.Module):
-    """ following @crowsonkb 's lead with learned sinusoidal pos emb """
+    """ following @crowsonkb 's lead with random (learned optional) sinusoidal pos emb """
     """ https://github.com/crowsonkb/v-diffusion-jax/blob/master/diffusion/models/danbooru_128.py#L8 """
 
-    def __init__(self, dim):
+    def __init__(self, dim, is_random = False):
         super().__init__()
         assert (dim % 2) == 0
         half_dim = dim // 2
-        self.weights = nn.Parameter(torch.randn(half_dim))
+        self.weights = nn.Parameter(torch.randn(half_dim), requires_grad = not is_random)
 
     def forward(self, x):
         x = rearrange(x, 'b -> b 1')
@@ -234,7 +234,7 @@ class LinearAttention(nn.Module):
         return self.to_out(out)
 
 class Attention(nn.Module):
-    def __init__(self, dim, heads = 4, dim_head = 32, scale = 10):
+    def __init__(self, dim, heads = 4, dim_head = 32):
         super().__init__()
         self.scale = dim_head ** -0.5
         self.heads = heads
@@ -271,6 +271,7 @@ class Unet(nn.Module):
         resnet_block_groups = 8,
         learned_variance = False,
         learned_sinusoidal_cond = False,
+        random_fourier_features = False,
         learned_sinusoidal_dim = 16
     ):
         super().__init__()
@@ -293,10 +294,10 @@ class Unet(nn.Module):
 
         time_dim = dim * 4
 
-        self.learned_sinusoidal_cond = learned_sinusoidal_cond
+        self.random_or_learned_sinusoidal_cond = learned_sinusoidal_cond or random_fourier_features
 
-        if learned_sinusoidal_cond:
+        if self.random_or_learned_sinusoidal_cond:
-            sinu_pos_emb = LearnedSinusoidalPosEmb(learned_sinusoidal_dim)
+            sinu_pos_emb = RandomOrLearnedSinusoidalPosEmb(learned_sinusoidal_dim, random_fourier_features)
             fourier_dim = learned_sinusoidal_dim + 1
         else:
             sinu_pos_emb = SinusoidalPosEmb(dim)
@@ -429,7 +430,7 @@ class GaussianDiffusion(nn.Module):
     ):
         super().__init__()
         assert not (type(self) == GaussianDiffusion and model.channels != model.out_dim)
-        assert not model.learned_sinusoidal_cond
+        assert not model.random_or_learned_sinusoidal_cond
 
         self.model = model
         self.channels = self.model.channels
@@ -439,7 +440,7 @@ class GaussianDiffusion(nn.Module):
 
         self.objective = objective
 
-        assert objective in {'pred_noise', 'pred_x0'}, 'objective must be either pred_noise (predict noise) or pred_x0 (predict image start)'
+        assert objective in {'pred_noise', 'pred_x0', 'pred_v'}, 'objective must be either pred_noise (predict noise) or pred_x0 (predict image start) or pred_v (predict v [v-parameterization as defined in appendix D of progressive distillation paper, used in imagen-video successfully])'
 
         if beta_schedule == 'linear':
             betas = linear_beta_schedule(timesteps)
@@ -510,6 +511,18 @@ class GaussianDiffusion(nn.Module):
             extract(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)
         )
 
+    def predict_v(self, x_start, t, noise):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_start.shape) * noise -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * x_start
+        )
+
+    def predict_start_from_v(self, x_t, t, v):
+        return (
+            extract(self.sqrt_alphas_cumprod, t, x_t.shape) * x_t -
+            extract(self.sqrt_one_minus_alphas_cumprod, t, x_t.shape) * v
+        )
+
     def q_posterior(self, x_start, x_t, t):
         posterior_mean = (
             extract(self.posterior_mean_coef1, t, x_t.shape) * x_start +
@@ -533,6 +546,12 @@ class GaussianDiffusion(nn.Module):
             x_start = maybe_clip(x_start)
             pred_noise = self.predict_noise_from_start(x, t, x_start)
 
+        elif self.objective == 'pred_v':
+            v = model_output
+            x_start = self.predict_start_from_v(x, t, v)
+            x_start = maybe_clip(x_start)
+            pred_noise = self.predict_noise_from_start(x, t, x_start)
+
         return ModelPrediction(pred_noise, x_start)
 
     def p_mean_variance(self, x, t, x_self_cond = None, clip_denoised = True):
@@ -670,6 +689,9 @@ class GaussianDiffusion(nn.Module):
             target = noise
         elif self.objective == 'pred_x0':
             target = x_start
+        elif self.objective == 'pred_v':
+            v = self.predict_v(x_start, t, noise)
+            target = v
         else:
             raise ValueError(f'unknown objective {self.objective}')
 

denoising_diffusion_pytorch/elucidated_diffusion.py

@@ -52,7 +52,7 @@ class ElucidatedDiffusion(nn.Module):
         S_noise = 1.003,
     ):
         super().__init__()
-        assert net.learned_sinusoidal_cond
+        assert net.random_or_learned_sinusoidal_cond
         self.self_condition = net.self_condition
 
         self.net = net

denoising_diffusion_pytorch/v_param_continuous_time_gaussian_diffusion.py

@@ -0,0 +1,184 @@
+import math
+import torch
+from torch import sqrt
+from torch import nn, einsum
+import torch.nn.functional as F
+from torch.special import expm1
+
+from tqdm import tqdm
+from einops import rearrange, repeat, reduce
+from einops.layers.torch import Rearrange
+
+# helpers
+
+def exists(val):
+    return val is not None
+
+def default(val, d):
+    if exists(val):
+        return val
+    return d() if callable(d) else d
+
+# normalization functions
+
+def normalize_to_neg_one_to_one(img):
+    return img * 2 - 1
+
+def unnormalize_to_zero_to_one(t):
+    return (t + 1) * 0.5
+
+# diffusion helpers
+
+def right_pad_dims_to(x, t):
+    padding_dims = x.ndim - t.ndim
+    if padding_dims <= 0:
+        return t
+    return t.view(*t.shape, *((1,) * padding_dims))
+
+# continuous schedules
+# log(snr) that approximates the original linear schedule
+
+def log(t, eps = 1e-20):
+    return torch.log(t.clamp(min = eps))
+
+def alpha_cosine_log_snr(t, s = 0.008):
+    return -log((torch.cos((t + s) / (1 + s) * math.pi * 0.5) ** -2) - 1, eps = 1e-5)
+
+class VParamContinuousTimeGaussianDiffusion(nn.Module):
+    """
+    a new type of parameterization in v-space proposed in https://arxiv.org/abs/2202.00512 that
+    (1) allows for improved distillation over noise prediction objective and
+    (2) noted in imagen-video to improve upsampling unets by removing the color shifting artifacts
+    """
+
+    def __init__(
+        self,
+        model,
+        *,
+        image_size,
+        channels = 3,
+        num_sample_steps = 500,
+        clip_sample_denoised = True,
+    ):
+        super().__init__()
+        assert model.random_or_learned_sinusoidal_cond
+        assert not model.self_condition, 'not supported yet'
+
+        self.model = model
+
+        # image dimensions
+
+        self.channels = channels
+        self.image_size = image_size
+
+        # continuous noise schedule related stuff
+
+        self.log_snr = alpha_cosine_log_snr
+
+        # sampling
+
+        self.num_sample_steps = num_sample_steps
+        self.clip_sample_denoised = clip_sample_denoised        
+
+    @property
+    def device(self):
+        return next(self.model.parameters()).device
+
+    def p_mean_variance(self, x, time, time_next):
+        # reviewer found an error in the equation in the paper (missing sigma)
+        # following - https://openreview.net/forum?id=2LdBqxc1Yv&noteId=rIQgH0zKsRt
+
+        log_snr = self.log_snr(time)
+        log_snr_next = self.log_snr(time_next)
+        c = -expm1(log_snr - log_snr_next)
+
+        squared_alpha, squared_alpha_next = log_snr.sigmoid(), log_snr_next.sigmoid()
+        squared_sigma, squared_sigma_next = (-log_snr).sigmoid(), (-log_snr_next).sigmoid()
+
+        alpha, sigma, alpha_next = map(sqrt, (squared_alpha, squared_sigma, squared_alpha_next))
+
+        batch_log_snr = repeat(log_snr, ' -> b', b = x.shape[0])
+
+        pred_v = self.model(x, batch_log_snr)
+
+        # shown in Appendix D in the paper
+        x_start = alpha * x - sigma * pred_v
+
+        if self.clip_sample_denoised:
+            x_start.clamp_(-1., 1.)
+
+        model_mean = alpha_next * (x * (1 - c) / alpha + c * x_start)
+
+        posterior_variance = squared_sigma_next * c
+
+        return model_mean, posterior_variance
+
+    # sampling related functions
+
+    @torch.no_grad()
+    def p_sample(self, x, time, time_next):
+        batch, *_, device = *x.shape, x.device
+
+        model_mean, model_variance = self.p_mean_variance(x = x, time = time, time_next = time_next)
+
+        if time_next == 0:
+            return model_mean
+
+        noise = torch.randn_like(x)
+        return model_mean + sqrt(model_variance) * noise
+
+    @torch.no_grad()
+    def p_sample_loop(self, shape):
+        batch = shape[0]
+
+        img = torch.randn(shape, device = self.device)
+        steps = torch.linspace(1., 0., self.num_sample_steps + 1, device = self.device)
+
+        for i in tqdm(range(self.num_sample_steps), desc = 'sampling loop time step', total = self.num_sample_steps):
+            times = steps[i]
+            times_next = steps[i + 1]
+            img = self.p_sample(img, times, times_next)
+
+        img.clamp_(-1., 1.)
+        img = unnormalize_to_zero_to_one(img)
+        return img
+
+    @torch.no_grad()
+    def sample(self, batch_size = 16):
+        return self.p_sample_loop((batch_size, self.channels, self.image_size, self.image_size))
+
+    # training related functions - noise prediction
+
+    def q_sample(self, x_start, times, noise = None):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        log_snr = self.log_snr(times)
+
+        log_snr_padded = right_pad_dims_to(x_start, log_snr)
+        alpha, sigma = sqrt(log_snr_padded.sigmoid()), sqrt((-log_snr_padded).sigmoid())
+        x_noised =  x_start * alpha + noise * sigma
+
+        return x_noised, log_snr, alpha, sigma
+
+    def random_times(self, batch_size):
+        return torch.zeros((batch_size,), device = self.device).float().uniform_(0, 1)
+
+    def p_losses(self, x_start, times, noise = None):
+        noise = default(noise, lambda: torch.randn_like(x_start))
+
+        x, log_snr, alpha, sigma = self.q_sample(x_start = x_start, times = times, noise = noise)
+
+        # described in section 4 as the prediction objective, with derivation in Appendix D
+        v = alpha * noise - sigma * x_start
+
+        model_out = self.model(x, log_snr)
+
+        return F.mse_loss(model_out, v)
+
+    def forward(self, img, *args, **kwargs):
+        b, c, h, w, device, img_size, = *img.shape, img.device, self.image_size
+        assert h == img_size and w == img_size, f'height and width of image must be {img_size}'
+
+        times = self.random_times(b)
+        img = normalize_to_neg_one_to_one(img)
+        return self.p_losses(img, times, *args, **kwargs)

setup.py

@@ -3,7 +3,7 @@ from setuptools import setup, find_packages
 setup(
   name = 'denoising-diffusion-pytorch',
   packages = find_packages(),
-  version = '0.28.0',
+  version = '0.30.0',
   license='MIT',
   description = 'Denoising Diffusion Probabilistic Models - Pytorch',
   author = 'Phil Wang',