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| import math | |
| import numpy as np | |
| from einops import repeat | |
| import torch | |
| import torch.nn.functional as F | |
| def timestep_embedding(timesteps, dim, max_period=10000, repeat_only=False): | |
| """ | |
| Create sinusoidal timestep embeddings. | |
| :param timesteps: a 1-D Tensor of N indices, one per batch element. | |
| These may be fractional. | |
| :param dim: the dimension of the output. | |
| :param max_period: controls the minimum frequency of the embeddings. | |
| :return: an [N x dim] Tensor of positional embeddings. | |
| """ | |
| if not repeat_only: | |
| half = dim // 2 | |
| freqs = torch.exp( | |
| -math.log(max_period) * torch.arange(start=0, end=half, dtype=torch.float32) / half | |
| ).to(device=timesteps.device) | |
| args = timesteps[:, None].float() * freqs[None] | |
| embedding = torch.cat([torch.cos(args), torch.sin(args)], dim=-1) | |
| if dim % 2: | |
| embedding = torch.cat([embedding, torch.zeros_like(embedding[:, :1])], dim=-1) | |
| else: | |
| embedding = repeat(timesteps, 'b -> b d', d=dim) | |
| return embedding | |
| def make_beta_schedule(schedule, n_timestep, linear_start=1e-4, linear_end=2e-2, cosine_s=8e-3): | |
| if schedule == "linear": | |
| betas = ( | |
| torch.linspace(linear_start ** 0.5, linear_end ** 0.5, n_timestep, dtype=torch.float64) ** 2 | |
| ) | |
| elif schedule == "cosine": | |
| timesteps = ( | |
| torch.arange(n_timestep + 1, dtype=torch.float64) / n_timestep + cosine_s | |
| ) | |
| alphas = timesteps / (1 + cosine_s) * np.pi / 2 | |
| alphas = torch.cos(alphas).pow(2) | |
| alphas = alphas / alphas[0] | |
| betas = 1 - alphas[1:] / alphas[:-1] | |
| betas = np.clip(betas, a_min=0, a_max=0.999) | |
| elif schedule == "sqrt_linear": | |
| betas = torch.linspace(linear_start, linear_end, n_timestep, dtype=torch.float64) | |
| elif schedule == "sqrt": | |
| betas = torch.linspace(linear_start, linear_end, n_timestep, dtype=torch.float64) ** 0.5 | |
| else: | |
| raise ValueError(f"schedule '{schedule}' unknown.") | |
| return betas.numpy() | |
| def make_ddim_timesteps(ddim_discr_method, num_ddim_timesteps, num_ddpm_timesteps, verbose=True): | |
| if ddim_discr_method == 'uniform': | |
| c = num_ddpm_timesteps // num_ddim_timesteps | |
| ddim_timesteps = np.asarray(list(range(0, num_ddpm_timesteps, c))) | |
| elif ddim_discr_method == 'quad': | |
| ddim_timesteps = ((np.linspace(0, np.sqrt(num_ddpm_timesteps * .8), num_ddim_timesteps)) ** 2).astype(int) | |
| else: | |
| raise NotImplementedError(f'There is no ddim discretization method called "{ddim_discr_method}"') | |
| # assert ddim_timesteps.shape[0] == num_ddim_timesteps | |
| # add one to get the final alpha values right (the ones from first scale to data during sampling) | |
| steps_out = ddim_timesteps + 1 | |
| if verbose: | |
| print(f'Selected timesteps for ddim sampler: {steps_out}') | |
| return steps_out | |
| def make_ddim_sampling_parameters(alphacums, ddim_timesteps, eta, verbose=True): | |
| # select alphas for computing the variance schedule | |
| # print(f'ddim_timesteps={ddim_timesteps}, len_alphacums={len(alphacums)}') | |
| alphas = alphacums[ddim_timesteps] | |
| alphas_prev = np.asarray([alphacums[0]] + alphacums[ddim_timesteps[:-1]].tolist()) | |
| # according the the formula provided in https://arxiv.org/abs/2010.02502 | |
| sigmas = eta * np.sqrt((1 - alphas_prev) / (1 - alphas) * (1 - alphas / alphas_prev)) | |
| if verbose: | |
| print(f'Selected alphas for ddim sampler: a_t: {alphas}; a_(t-1): {alphas_prev}') | |
| print(f'For the chosen value of eta, which is {eta}, ' | |
| f'this results in the following sigma_t schedule for ddim sampler {sigmas}') | |
| return sigmas, alphas, alphas_prev | |
| def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999): | |
| """ | |
| Create a beta schedule that discretizes the given alpha_t_bar function, | |
| which defines the cumulative product of (1-beta) over time from t = [0,1]. | |
| :param num_diffusion_timesteps: the number of betas to produce. | |
| :param alpha_bar: a lambda that takes an argument t from 0 to 1 and | |
| produces the cumulative product of (1-beta) up to that | |
| part of the diffusion process. | |
| :param max_beta: the maximum beta to use; use values lower than 1 to | |
| prevent singularities. | |
| """ | |
| betas = [] | |
| for i in range(num_diffusion_timesteps): | |
| t1 = i / num_diffusion_timesteps | |
| t2 = (i + 1) / num_diffusion_timesteps | |
| betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta)) | |
| return np.array(betas) |