dmme.equations.ddpm

linear_schedule	constants increasing linearly from \(10^{-4}\) to \(0.02\)
forward_process	Forward Process, \(q(x_t|x_{t-1})\)
reverse_process	Reverse Denoising Process, \(p_\theta(x_{t-1}|x_t)\)
simple_loss	Simple Loss objective \(L_\text{simple}\), MSE loss between noise and predicted noise

dmme.equations.ddpm.linear_schedule(timesteps: int, start: float = 0.0001, end: float = 0.02) → Tensor

constants increasing linearly from \(10^{-4}\) to \(0.02\)

Parameters:

• timesteps – total timesteps

• start – starting value, defaults to 0.0001

• end – end value, defaults to 0.02

Returns:

a 1d tensor representing \(\beta_t\) indexed by \(t\)

dmme.equations.ddpm.forward_process(image: Tensor, alpha_bar_t: Tensor) → Normal

Forward Process, \(q(x_t|x_{t-1})\)

Parameters:

• image – image of shape \((N, C, H, W)\)

• alpha_bar_t – \(\bar\alpha_t\) of shape \((N, 1, 1, *)\)

• noise – noise sampled from standard normal distribution with the same shape as the image

Returns:

gaussian transition distirbution \(q(x_t|x_{t-1})\)

dmme.equations.ddpm.reverse_process(x_t: Tensor, beta_t: Tensor, alpha_t: Tensor, alpha_bar_t: Tensor, noise_in_x_t: Tensor, variance: Tensor) → Normal

Reverse Denoising Process, \(p_\theta(x_{t-1}|x_t)\)

Parameters:

• beta_t – \(\beta_t\) of shape \((N, 1, 1, *)\)

• alpha_t – \(\alpha_t\) of shape \((N, 1, 1, *)\)

• alpha_bar_t – \(\bar\alpha_t\) of shape \((N, 1, 1, *)\)

• noise_in_x_t – estimated noise in \(x_t\) predicted by a neural network

• variance – variance of the reverse process, either learned or fixed

• noise – noise sampled from \(\mathcal{N}(0, I)\)

Returns:

denoising distirbution \(q(x_t|x_{t-1})\)

dmme.equations.ddpm.simple_loss(noise: Tensor, estimated_noise: Tensor) → Tensor

Simple Loss objective \(L_\text{simple}\), MSE loss between noise and predicted noise

Parameters:

• noise (torch.Tensor) – noise used in the forward process

• estimated_noise (torch.Tensor) – estimated noise with the same shape as noise