# -------------------------------------------------------- # Adapted from: https://github.com/openai/point-e # Licensed under the MIT License # Copyright (c) 2022 OpenAI # Permission is hereby granted, free of charge, to any person obtaining a copy # of this software and associated documentation files (the "Software"), to deal # in the Software without restriction, including without limitation the rights # to use, copy, modify, merge, publish, distribute, sublicense, and/or sell # copies of the Software, and to permit persons to whom the Software is # furnished to do so, subject to the following conditions: # The above copyright notice and this permission notice shall be included in all # copies or substantial portions of the Software. # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, # FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE # AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER # LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE # SOFTWARE. # -------------------------------------------------------- import math from typing import Any, Dict, Iterable, Optional, Sequence, Union import numpy as np import torch as th def sigmoid_schedule(t, start=-3, end=3, tau=0.6, clip_min=1e-9): def sigmoid(x): return 1 / (1 + np.exp(-x)) v_start = sigmoid(start / tau) v_end = sigmoid(end / tau) output = sigmoid((t * (end - start) + start) / tau) output = (v_end - output) / (v_end - v_start) return np.clip(output, clip_min, 1.0) def get_beta_schedule(beta_schedule, *, beta_start, beta_end, num_diffusion_timesteps): """ This is the deprecated API for creating beta schedules. See get_named_beta_schedule() for the new library of schedules. """ if beta_schedule == "linear": betas = np.linspace( beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64 ) else: raise NotImplementedError(beta_schedule) assert betas.shape == (num_diffusion_timesteps,) return betas def get_named_beta_schedule(schedule_name, num_diffusion_timesteps, exp_p=12): """ Get a pre-defined beta schedule for the given name. The beta schedule library consists of beta schedules which remain similar in the limit of num_diffusion_timesteps. Beta schedules may be added, but should not be removed or changed once they are committed to maintain backwards compatibility. """ if schedule_name == "linear": # Linear schedule from Ho et al, extended to work for any number of # diffusion steps. scale = 1000 / num_diffusion_timesteps return get_beta_schedule( "linear", beta_start=scale * 0.0001, beta_end=scale * 0.02, num_diffusion_timesteps=num_diffusion_timesteps, ) elif schedule_name == "cosine": return betas_for_alpha_bar( num_diffusion_timesteps, lambda t: math.cos((t + 0.008) / 1.008 * math.pi / 2) ** 2, ) elif schedule_name == "sigmoid": # Sigmoid schedule passed through betas_for_alpha_bar return betas_for_alpha_bar( num_diffusion_timesteps, lambda t: sigmoid_schedule(t) ) else: raise NotImplementedError(f"unknown beta schedule: {schedule_name}") 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) def space_timesteps(num_timesteps, section_counts): """ Create a list of timesteps to use from an original diffusion process, given the number of timesteps we want to take from equally-sized portions of the original process. For example, if there's 300 timesteps and the section counts are [10,15,20] then the first 100 timesteps are strided to be 10 timesteps, the second 100 are strided to be 15 timesteps, and the final 100 are strided to be 20. :param num_timesteps: the number of diffusion steps in the original process to divide up. :param section_counts: either a list of numbers, or a string containing comma-separated numbers, indicating the step count per section. As a special case, use "ddimN" where N is a number of steps to use the striding from the DDIM paper. :return: a set of diffusion steps from the original process to use. """ if isinstance(section_counts, str): if section_counts.startswith("ddim"): desired_count = int(section_counts[len("ddim") :]) for i in range(1, num_timesteps): if len(range(0, num_timesteps, i)) == desired_count: return set(range(0, num_timesteps, i)) raise ValueError( f"cannot create exactly {num_timesteps} steps with an integer stride" ) elif section_counts.startswith("exact"): res = set(int(x) for x in section_counts[len("exact") :].split(",")) for x in res: if x < 0 or x >= num_timesteps: raise ValueError(f"timestep out of bounds: {x}") return res section_counts = [int(x) for x in section_counts.split(",")] size_per = num_timesteps // len(section_counts) extra = num_timesteps % len(section_counts) start_idx = 0 all_steps = [] for i, section_count in enumerate(section_counts): size = size_per + (1 if i < extra else 0) if size < section_count: raise ValueError( f"cannot divide section of {size} steps into {section_count}" ) if section_count <= 1: frac_stride = 1 else: frac_stride = (size - 1) / (section_count - 1) cur_idx = 0.0 taken_steps = [] for _ in range(section_count): taken_steps.append(start_idx + round(cur_idx)) cur_idx += frac_stride all_steps += taken_steps start_idx += size return set(all_steps) def _extract_into_tensor(arr, timesteps, broadcast_shape): """Extract values from a 1-D numpy array for a batch of indices.""" res = th.from_numpy(arr).to(device=timesteps.device)[timesteps].float() while len(res.shape) < len(broadcast_shape): res = res[..., None] return res + th.zeros(broadcast_shape, device=timesteps.device) class GaussianDiffusion: """ Utilities for sampling from Gaussian diffusion models. """ def __init__( self, *, betas: Sequence[float], model_mean_type: str, model_var_type: str, channel_scales: Optional[np.ndarray] = None, channel_biases: Optional[np.ndarray] = None, ): self.model_mean_type = model_mean_type self.model_var_type = model_var_type self.channel_scales = channel_scales self.channel_biases = channel_biases # Use float64 for accuracy betas = np.array(betas, dtype=np.float64) self.betas = betas assert len(betas.shape) == 1, "betas must be 1-D" assert (betas > 0).all() and (betas <= 1).all() self.num_timesteps = int(betas.shape[0]) alphas = 1.0 - betas self.alphas_cumprod = np.cumprod(alphas, axis=0) self.alphas_cumprod_prev = np.append(1.0, self.alphas_cumprod[:-1]) # calculations for diffusion q(x_t | x_{t-1}) and others self.sqrt_alphas_cumprod = np.sqrt(self.alphas_cumprod) self.sqrt_one_minus_alphas_cumprod = np.sqrt(1.0 - self.alphas_cumprod) self.sqrt_recip_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod) self.sqrt_recipm1_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod - 1) # calculations for posterior q(x_{t-1} | x_t, x_0) self.posterior_variance = ( betas * (1.0 - self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod) ) # below: log calculation clipped because the posterior variance is 0 at the beginning of the diffusion chain self.posterior_log_variance_clipped = np.log( np.append(self.posterior_variance[1], self.posterior_variance[1:]) ) self.posterior_mean_coef1 = ( betas * np.sqrt(self.alphas_cumprod_prev) / (1.0 - self.alphas_cumprod) ) self.posterior_mean_coef2 = ( (1.0 - self.alphas_cumprod_prev) * np.sqrt(alphas) / (1.0 - self.alphas_cumprod) ) def scale_channels(self, x: th.Tensor) -> th.Tensor: """Apply channel-wise scaling.""" if self.channel_scales is not None: x = x * th.from_numpy(self.channel_scales).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) if self.channel_biases is not None: x = x + th.from_numpy(self.channel_biases).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) return x def unscale_channels(self, x: th.Tensor) -> th.Tensor: """Remove channel-wise scaling.""" if self.channel_biases is not None: x = x - th.from_numpy(self.channel_biases).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) if self.channel_scales is not None: x = x / th.from_numpy(self.channel_scales).to(x).reshape( [1, -1, *([1] * (len(x.shape) - 2))] ) return x def unscale_out_dict( self, out: Dict[str, Union[th.Tensor, Any]] ) -> Dict[str, Union[th.Tensor, Any]]: return { k: (self.unscale_channels(v) if isinstance(v, th.Tensor) else v) for k, v in out.items() } def q_posterior_mean_variance(self, x_start, x_t, t): """ Compute the mean and variance of the diffusion posterior: q(x_{t-1} | x_t, x_0) """ assert x_start.shape == x_t.shape posterior_mean = ( _extract_into_tensor(self.posterior_mean_coef1, t, x_t.shape) * x_start + _extract_into_tensor(self.posterior_mean_coef2, t, x_t.shape) * x_t ) posterior_variance = _extract_into_tensor(self.posterior_variance, t, x_t.shape) posterior_log_variance_clipped = _extract_into_tensor( self.posterior_log_variance_clipped, t, x_t.shape ) assert ( posterior_mean.shape[0] == posterior_variance.shape[0] == posterior_log_variance_clipped.shape[0] == x_start.shape[0] ) return posterior_mean, posterior_variance, posterior_log_variance_clipped def p_mean_variance( self, model, x, t, clip_denoised=True, denoised_fn=None, model_kwargs=None ): """ Apply the model to get p(x_{t-1} | x_t). """ if model_kwargs is None: model_kwargs = {} B, C = x.shape[:2] assert t.shape == (B,) # Direct prediction of eps model_output = model(x, t, **model_kwargs) if isinstance(model_output, tuple): model_output, prev_latent = model_output model_kwargs["prev_latent"] = prev_latent # Convert model output to mean and variance model_variance, model_log_variance = { # for fixedlarge, we set the initial (log-)variance like so # to get a better decoder log likelihood. "fixed_large": ( np.append(self.posterior_variance[1], self.betas[1:]), np.log(np.append(self.posterior_variance[1], self.betas[1:])), ), "fixed_small": ( self.posterior_variance, self.posterior_log_variance_clipped, ), }[self.model_var_type] model_variance = _extract_into_tensor(model_variance, t, x.shape) model_log_variance = _extract_into_tensor(model_log_variance, t, x.shape) def process_xstart(x): if denoised_fn is not None: x = denoised_fn(x) if clip_denoised: x = x.clamp( -self.channel_scales[0] * 0.67, self.channel_scales[0] * 0.67 ) x[:, 3:] = x[:, 3:].clamp( -self.channel_scales[3] * 0.5, self.channel_scales[3] * 0.5 ) return x return x if self.model_mean_type == "x_prev": pred_xstart = process_xstart( self._predict_xstart_from_xprev(x_t=x, t=t, xprev=model_output) ) model_mean = model_output elif self.model_mean_type in ["x_start", "epsilon"]: if self.model_mean_type == "x_start": pred_xstart = process_xstart(model_output) else: pred_xstart = process_xstart( self._predict_xstart_from_eps(x_t=x, t=t, eps=model_output) ) model_mean, _, _ = self.q_posterior_mean_variance( x_start=pred_xstart, x_t=x, t=t ) # print('p_mean_variance:', pred_xstart.min(), pred_xstart.max()) else: raise NotImplementedError(self.model_mean_type) assert ( model_mean.shape == model_log_variance.shape == pred_xstart.shape == x.shape ) return { "mean": model_mean, "variance": model_variance, "log_variance": model_log_variance, "pred_xstart": pred_xstart, } def _predict_xstart_from_eps(self, x_t, t, eps): assert x_t.shape == eps.shape return ( _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) * eps ) def _predict_xstart_from_xprev(self, x_t, t, xprev): assert x_t.shape == xprev.shape return ( # (xprev - coef2*x_t) / coef1 _extract_into_tensor(1.0 / self.posterior_mean_coef1, t, x_t.shape) * xprev - _extract_into_tensor( self.posterior_mean_coef2 / self.posterior_mean_coef1, t, x_t.shape ) * x_t ) def _predict_eps_from_xstart(self, x_t, t, pred_xstart): return ( _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - pred_xstart ) / _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) def ddim_sample_loop_progressive( self, model, shape, noise=None, clip_denoised=True, denoised_fn=None, model_kwargs=None, device=None, progress=False, eta=0.0, ): """ Use DDIM to sample from the model and yield intermediate samples. """ if device is None: device = next(model.parameters()).device assert isinstance(shape, (tuple, list)) if noise is not None: img = noise else: img = th.randn(*shape, device=device) indices = list(range(self.num_timesteps))[::-1] if progress: from tqdm.auto import tqdm indices = tqdm(indices) for i in indices: t = th.tensor([i] * shape[0], device=device) with th.no_grad(): out = self.ddim_sample( model, img, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, model_kwargs=model_kwargs, eta=eta, ) yield self.unscale_out_dict(out) img = out["sample"] def _predict_eps_from_xstart(self, x_t, t, pred_xstart): return ( _extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x_t.shape) * x_t - pred_xstart ) / _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t, x_t.shape) def ddim_sample( self, model, x, t, clip_denoised=True, denoised_fn=None, model_kwargs=None, eta=0.0, ): """ Sample x_{t-1} from the model using DDIM. """ out = self.p_mean_variance( model, x, t, clip_denoised=clip_denoised, denoised_fn=denoised_fn, model_kwargs=model_kwargs, ) # Usually our model outputs epsilon, but we re-derive it # in case we used x_start or x_prev prediction. eps = self._predict_eps_from_xstart(x, t, out["pred_xstart"]) alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape) alpha_bar_prev = _extract_into_tensor(self.alphas_cumprod_prev, t, x.shape) sigma = ( eta * th.sqrt((1 - alpha_bar_prev) / (1 - alpha_bar)) * th.sqrt(1 - alpha_bar / alpha_bar_prev) ) # Equation 12. noise = th.randn_like(x) mean_pred = ( out["pred_xstart"] * th.sqrt(alpha_bar_prev) + th.sqrt(1 - alpha_bar_prev - sigma**2) * eps ) nonzero_mask = (t != 0).float().view(-1, *([1] * (len(x.shape) - 1))) sample = mean_pred + nonzero_mask * sigma * noise return {"sample": sample, "pred_xstart": out["pred_xstart"]} class SpacedDiffusion(GaussianDiffusion): """ A diffusion process which can skip steps in a base diffusion process. """ def __init__(self, use_timesteps: Iterable[int], **kwargs): self.use_timesteps = set(use_timesteps) self.timestep_map = [] self.original_num_steps = len(kwargs["betas"]) base_diffusion = GaussianDiffusion(**kwargs) last_alpha_cumprod = 1.0 new_betas = [] for i, alpha_cumprod in enumerate(base_diffusion.alphas_cumprod): if i in self.use_timesteps: new_betas.append(1 - alpha_cumprod / last_alpha_cumprod) last_alpha_cumprod = alpha_cumprod self.timestep_map.append(i) kwargs["betas"] = np.array(new_betas) super().__init__(**kwargs) def p_mean_variance(self, model, *args, **kwargs): return super().p_mean_variance(self._wrap_model(model), *args, **kwargs) def _wrap_model(self, model): if isinstance(model, _WrappedModel): return model return _WrappedModel(model, self.timestep_map, self.original_num_steps) class _WrappedModel: """Helper class to wrap models for SpacedDiffusion.""" def __init__(self, model, timestep_map, original_num_steps): self.model = model self.timestep_map = timestep_map self.original_num_steps = original_num_steps def __call__(self, x, ts, **kwargs): map_tensor = th.tensor(self.timestep_map, device=ts.device, dtype=ts.dtype) new_ts = map_tensor[ts] return self.model(x, new_ts, **kwargs)