from inspect import isfunction import numpy as np import torch import torch.nn.functional as F from tqdm import tqdm def exists(x): return x is not None def default(val, d): if exists(val): return val return d() if isfunction(d) else d def noise_like(shape, device, repeat=False): repeat_noise = lambda: torch.randn((1, *shape[1:]), device=device).repeat(shape[0], *((1,) * (len(shape) - 1))) noise = lambda: torch.randn(shape, device=device) return repeat_noise() if repeat else noise() def extract(a, t, x_shape): b, *_ = t.shape out = a.gather(-1, t) return out.reshape(b, *((1,) * (len(x_shape) - 1))) def make_ddim_sampling_parameters(alphacums, ddim_timesteps, eta, verbose=True): # select alphas for computing the variance schedule 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 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 class DDIMSampler(object): def __init__(self, model, schedule="linear", **kwargs): super().__init__() self.model = model self.ddpm_num_timesteps = model.num_timesteps self.schedule = schedule def register_buffer(self, name, attr): if type(attr) == torch.Tensor: if attr.device != torch.device("cpu"): attr = attr.to(torch.device("cpu")) setattr(self, name, attr) def make_schedule(self, ddim_num_steps, ddim_discretize="uniform", ddim_eta=0., verbose=True): self.ddim_timesteps = make_ddim_timesteps(ddim_discr_method=ddim_discretize, num_ddim_timesteps=ddim_num_steps, num_ddpm_timesteps=self.ddpm_num_timesteps, verbose=verbose) alphas_cumprod = self.model.alphas_cumprod assert alphas_cumprod.shape[0] == self.ddpm_num_timesteps, 'alphas have to be defined for each timestep' to_torch = lambda x: x.clone().detach().to(torch.float32).to(torch.device("cpu")) self.register_buffer('betas', to_torch(self.model.betas)) self.register_buffer('alphas_cumprod', to_torch(alphas_cumprod)) self.register_buffer('alphas_cumprod_prev', to_torch(self.model.alphas_cumprod_prev)) # calculations for diffusion q(x_t | x_{t-1}) and others self.register_buffer('sqrt_alphas_cumprod', to_torch(np.sqrt(alphas_cumprod.cpu()))) self.register_buffer('sqrt_one_minus_alphas_cumprod', to_torch(np.sqrt(1. - alphas_cumprod.cpu()))) self.register_buffer('log_one_minus_alphas_cumprod', to_torch(np.log(1. - alphas_cumprod.cpu()))) self.register_buffer('sqrt_recip_alphas_cumprod', to_torch(np.sqrt(1. / alphas_cumprod.cpu()))) self.register_buffer('sqrt_recipm1_alphas_cumprod', to_torch(np.sqrt(1. / alphas_cumprod.cpu() - 1))) # ddim sampling parameters ddim_sigmas, ddim_alphas, ddim_alphas_prev = make_ddim_sampling_parameters(alphacums=alphas_cumprod.cpu(), ddim_timesteps=self.ddim_timesteps, eta=ddim_eta, verbose=verbose) self.register_buffer('ddim_sigmas', ddim_sigmas) self.register_buffer('ddim_alphas', ddim_alphas) self.register_buffer('ddim_alphas_prev', ddim_alphas_prev) self.register_buffer('ddim_sqrt_one_minus_alphas', np.sqrt(1. - ddim_alphas)) sigmas_for_original_sampling_steps = ddim_eta * torch.sqrt( (1 - self.alphas_cumprod_prev) / (1 - self.alphas_cumprod) * ( 1 - self.alphas_cumprod / self.alphas_cumprod_prev)) self.register_buffer('ddim_sigmas_for_original_num_steps', sigmas_for_original_sampling_steps) @torch.no_grad() def sample(self, S, batch_size, shape, conditioning=None, callback=None, img_callback=None, quantize_x0=False, eta=0., mask=None, x0=None, temperature=1., noise_dropout=0., score_corrector=None, corrector_kwargs=None, verbose=True, x_T=None, log_every_t=100, **kwargs ): self.make_schedule(ddim_num_steps=S, ddim_eta=eta, verbose=verbose) # sampling C, H, W, D = shape size = (batch_size, C, H, W, D) print(f'Data shape for DDIM sampling is {size}, eta {eta}') samples, intermediates = self.ddim_sampling( conditioning, size, callback=callback, img_callback=img_callback, quantize_denoised=quantize_x0, mask=mask, x0=x0, ddim_use_original_steps=False, noise_dropout=noise_dropout, temperature=temperature, score_corrector=score_corrector, corrector_kwargs=corrector_kwargs, x_T=x_T, log_every_t=log_every_t ) return samples, intermediates @torch.no_grad() def ddim_sampling(self, cond, shape, x_T=None, ddim_use_original_steps=False, callback=None, timesteps=None, quantize_denoised=False, mask=None, x0=None, img_callback=None, log_every_t=100, temperature=1., noise_dropout=0., score_corrector=None, corrector_kwargs=None): device = self.model.betas.device b = shape[0] if x_T is None: img = torch.randn(shape, device=device) else: img = x_T if timesteps is None: timesteps = self.ddpm_num_timesteps if ddim_use_original_steps else self.ddim_timesteps elif timesteps is not None and not ddim_use_original_steps: subset_end = int(min(timesteps / self.ddim_timesteps.shape[0], 1) * self.ddim_timesteps.shape[0]) - 1 timesteps = self.ddim_timesteps[:subset_end] intermediates = {'x_inter': [img], 'pred_x0': [img]} time_range = reversed(range(0, timesteps)) if ddim_use_original_steps else np.flip(timesteps) total_steps = timesteps if ddim_use_original_steps else timesteps.shape[0] print(f"Running DDIM Sampling with {total_steps} timesteps") iterator = tqdm(time_range, desc='DDIM Sampler', total=total_steps) for i, step in enumerate(iterator): index = total_steps - i - 1 ts = torch.full((b,), step, device=device, dtype=torch.long) if mask is not None: assert x0 is not None img_orig = self.model.q_sample(x0, ts) # TODO: deterministic forward pass? img = img_orig * mask + (1. - mask) * img outs = self.p_sample_ddim(img, cond, ts, index=index, use_original_steps=ddim_use_original_steps, quantize_denoised=quantize_denoised, temperature=temperature, noise_dropout=noise_dropout, score_corrector=score_corrector, corrector_kwargs=corrector_kwargs) img, pred_x0 = outs if callback: callback(i) if img_callback: img_callback(pred_x0, i) if index % log_every_t == 0 or index == total_steps - 1: intermediates['x_inter'].append(img) intermediates['pred_x0'].append(pred_x0) return img, intermediates @torch.no_grad() def p_sample_ddim(self, x, c, t, index, repeat_noise=False, use_original_steps=False, quantize_denoised=False, temperature=1., noise_dropout=0., score_corrector=None, corrector_kwargs=None): b, *_, device = *x.shape, x.device e_t = self.model.apply_model(x, t, c) if score_corrector is not None: assert self.model.parameterization == "eps" e_t = score_corrector.modify_score(self.model, e_t, x, t, c, **corrector_kwargs) alphas = self.model.alphas_cumprod if use_original_steps else self.ddim_alphas alphas_prev = self.model.alphas_cumprod_prev if use_original_steps else self.ddim_alphas_prev sqrt_one_minus_alphas = self.model.sqrt_one_minus_alphas_cumprod if use_original_steps else self.ddim_sqrt_one_minus_alphas sigmas = self.model.ddim_sigmas_for_original_num_steps if use_original_steps else self.ddim_sigmas # select parameters corresponding to the currently considered timestep a_t = torch.full((b, 1, 1, 1, 1), alphas[index], device=device) a_prev = torch.full((b, 1, 1, 1, 1), alphas_prev[index], device=device) sigma_t = torch.full((b, 1, 1, 1, 1), sigmas[index], device=device) sqrt_one_minus_at = torch.full((b, 1, 1, 1, 1), sqrt_one_minus_alphas[index], device=device) # current prediction for x_0 pred_x0 = (x - sqrt_one_minus_at * e_t) / a_t.sqrt() if quantize_denoised: pred_x0, _, *_ = self.model.first_stage_model.quantize(pred_x0) # direction pointing to x_t dir_xt = (1. - a_prev - sigma_t ** 2).sqrt() * e_t noise = sigma_t * noise_like(x.shape, device, repeat_noise) * temperature if noise_dropout > 0.: noise = torch.nn.functional.dropout(noise, p=noise_dropout) x_prev = a_prev.sqrt() * pred_x0 + dir_xt + noise return x_prev, pred_x0