take care of equation 7 in the paper

denoising_diffusion_pytorch/elucidated_diffusion.py

@@ -37,6 +37,7 @@ def __init__(
         *,
         image_size,
         channels = 3,
+        num_sample_steps = 32, # number of sampling steps
         sigma_min = 0.002,     # min noise level
         sigma_max = 80,        # max noise level
         sigma_data = 0.5,      # standard deviation of data distribution
@@ -46,7 +47,7 @@ def __init__(
         S_churn = 80,          # parameters for stochastic sampling - depends on dataset, Table 5 in apper
         S_tmin = 0.05,
         S_tmax = 50,
-        S_noise = 1.003
+        S_noise = 1.003,
     ):
         super().__init__()
         assert net.learned_sinusoidal_cond
@@ -69,6 +70,8 @@ def __init__(
         self.P_mean = P_mean
         self.P_std = P_std
 
+        self.num_sample_steps = num_sample_steps  # otherwise known as N in the paper
+
         self.S_churn = S_churn
         self.S_tmin = S_tmin
         self.S_tmax = S_tmax
@@ -101,6 +104,23 @@ def noise_distribution(self, batch_size):
     def loss_weight(self, sigma):
         return (sigma ** 2 + self.sigma_data ** 2) * (sigma * self.sigma_data) ** -2
 
+    # sample schedule
+    # equation (5) in the paper
+
+    def sample_schedule(self, num_sample_steps = None):
+        num_sample_steps = default(num_sample_steps, self.num_sample_steps)
+
+        rho, sigma_max, sigma_min = self.rho, self.sigma_max, self.sigma_min
+
+        N = num_sample_steps
+        inv_rho = 1 / rho
+
+        for i in range(num_sample_steps - 1):
+            next_sigma = (sigma_max ** inv_rho + i / (N - 1) * (sigma_min ** inv_rho - sigma_max ** inv_rho)) ** rho
+            yield next_sigma
+
+        yield 0. # last step return 0.
+
     # preconditioned network output
     # equation (7) in the paper
 
@@ -121,11 +141,11 @@ def sample(self, batch_size = 16):
         shape = (batch_size, self.channels, self.image_size, self.image_size)
 
         images = torch.randn(shape, device = self.device)
-        steps = torch.linspace(1., 0., 100 + 1, device = self.device)
 
-        for i in tqdm(range(100), desc = 'sampling loop time step', total = 100):
-            times = steps[i]
-            times_next = steps[i + 1]
+        sigma_schedule = [*self.sample_schedule()]
+        sigma_schedule = list(zip(sigma_schedule[:-1], sigma_schedule[1:]))
+
+        for sigma, sigma_next in tqdm(sigma_schedule, desc = 'sampling time step'):
             images = images
 
         return unnormalize_to_zero_to_one(images)