# Copyright 2023 Microsoft and The HuggingFace Team. All rights reserved. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. from dataclasses import dataclass from typing import Optional, Tuple, Union import numpy as np import torch import torch.nn.functional as F from ..configuration_utils import ConfigMixin, register_to_config from ..utils import BaseOutput from .scheduling_utils import SchedulerMixin @dataclass class VQDiffusionSchedulerOutput(BaseOutput): """ Output class for the scheduler's step function output. Args: prev_sample (`torch.LongTensor` of shape `(batch size, num latent pixels)`): Computed sample x_{t-1} of previous timestep. `prev_sample` should be used as next model input in the denoising loop. """ prev_sample: torch.LongTensor def index_to_log_onehot(x: torch.LongTensor, num_classes: int) -> torch.FloatTensor: """ Convert batch of vector of class indices into batch of log onehot vectors Args: x (`torch.LongTensor` of shape `(batch size, vector length)`): Batch of class indices num_classes (`int`): number of classes to be used for the onehot vectors Returns: `torch.FloatTensor` of shape `(batch size, num classes, vector length)`: Log onehot vectors """ x_onehot = F.one_hot(x, num_classes) x_onehot = x_onehot.permute(0, 2, 1) log_x = torch.log(x_onehot.float().clamp(min=1e-30)) return log_x def gumbel_noised(logits: torch.FloatTensor, generator: Optional[torch.Generator]) -> torch.FloatTensor: """ Apply gumbel noise to `logits` """ uniform = torch.rand(logits.shape, device=logits.device, generator=generator) gumbel_noise = -torch.log(-torch.log(uniform + 1e-30) + 1e-30) noised = gumbel_noise + logits return noised def alpha_schedules(num_diffusion_timesteps: int, alpha_cum_start=0.99999, alpha_cum_end=0.000009): """ Cumulative and non-cumulative alpha schedules. See section 4.1. """ att = ( np.arange(0, num_diffusion_timesteps) / (num_diffusion_timesteps - 1) * (alpha_cum_end - alpha_cum_start) + alpha_cum_start ) att = np.concatenate(([1], att)) at = att[1:] / att[:-1] att = np.concatenate((att[1:], [1])) return at, att def gamma_schedules(num_diffusion_timesteps: int, gamma_cum_start=0.000009, gamma_cum_end=0.99999): """ Cumulative and non-cumulative gamma schedules. See section 4.1. """ ctt = ( np.arange(0, num_diffusion_timesteps) / (num_diffusion_timesteps - 1) * (gamma_cum_end - gamma_cum_start) + gamma_cum_start ) ctt = np.concatenate(([0], ctt)) one_minus_ctt = 1 - ctt one_minus_ct = one_minus_ctt[1:] / one_minus_ctt[:-1] ct = 1 - one_minus_ct ctt = np.concatenate((ctt[1:], [0])) return ct, ctt class VQDiffusionScheduler(SchedulerMixin, ConfigMixin): """ A scheduler for vector quantized diffusion. This model inherits from [`SchedulerMixin`] and [`ConfigMixin`]. Check the superclass documentation for the generic methods the library implements for all schedulers such as loading and saving. Args: num_vec_classes (`int`): The number of classes of the vector embeddings of the latent pixels. Includes the class for the masked latent pixel. num_train_timesteps (`int`, defaults to 100): The number of diffusion steps to train the model. alpha_cum_start (`float`, defaults to 0.99999): The starting cumulative alpha value. alpha_cum_end (`float`, defaults to 0.00009): The ending cumulative alpha value. gamma_cum_start (`float`, defaults to 0.00009): The starting cumulative gamma value. gamma_cum_end (`float`, defaults to 0.99999): The ending cumulative gamma value. """ order = 1 @register_to_config def __init__( self, num_vec_classes: int, num_train_timesteps: int = 100, alpha_cum_start: float = 0.99999, alpha_cum_end: float = 0.000009, gamma_cum_start: float = 0.000009, gamma_cum_end: float = 0.99999, ): self.num_embed = num_vec_classes # By convention, the index for the mask class is the last class index self.mask_class = self.num_embed - 1 at, att = alpha_schedules(num_train_timesteps, alpha_cum_start=alpha_cum_start, alpha_cum_end=alpha_cum_end) ct, ctt = gamma_schedules(num_train_timesteps, gamma_cum_start=gamma_cum_start, gamma_cum_end=gamma_cum_end) num_non_mask_classes = self.num_embed - 1 bt = (1 - at - ct) / num_non_mask_classes btt = (1 - att - ctt) / num_non_mask_classes at = torch.tensor(at.astype("float64")) bt = torch.tensor(bt.astype("float64")) ct = torch.tensor(ct.astype("float64")) log_at = torch.log(at) log_bt = torch.log(bt) log_ct = torch.log(ct) att = torch.tensor(att.astype("float64")) btt = torch.tensor(btt.astype("float64")) ctt = torch.tensor(ctt.astype("float64")) log_cumprod_at = torch.log(att) log_cumprod_bt = torch.log(btt) log_cumprod_ct = torch.log(ctt) self.log_at = log_at.float() self.log_bt = log_bt.float() self.log_ct = log_ct.float() self.log_cumprod_at = log_cumprod_at.float() self.log_cumprod_bt = log_cumprod_bt.float() self.log_cumprod_ct = log_cumprod_ct.float() # setable values self.num_inference_steps = None self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy()) def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None): """ Sets the discrete timesteps used for the diffusion chain (to be run before inference). Args: num_inference_steps (`int`): The number of diffusion steps used when generating samples with a pre-trained model. device (`str` or `torch.device`, *optional*): The device to which the timesteps and diffusion process parameters (alpha, beta, gamma) should be moved to. """ self.num_inference_steps = num_inference_steps timesteps = np.arange(0, self.num_inference_steps)[::-1].copy() self.timesteps = torch.from_numpy(timesteps).to(device) self.log_at = self.log_at.to(device) self.log_bt = self.log_bt.to(device) self.log_ct = self.log_ct.to(device) self.log_cumprod_at = self.log_cumprod_at.to(device) self.log_cumprod_bt = self.log_cumprod_bt.to(device) self.log_cumprod_ct = self.log_cumprod_ct.to(device) def step( self, model_output: torch.FloatTensor, timestep: torch.long, sample: torch.LongTensor, generator: Optional[torch.Generator] = None, return_dict: bool = True, ) -> Union[VQDiffusionSchedulerOutput, Tuple]: """ Predict the sample from the previous timestep by the reverse transition distribution. See [`~VQDiffusionScheduler.q_posterior`] for more details about how the distribution is computer. Args: log_p_x_0: (`torch.FloatTensor` of shape `(batch size, num classes - 1, num latent pixels)`): The log probabilities for the predicted classes of the initial latent pixels. Does not include a prediction for the masked class as the initial unnoised image cannot be masked. t (`torch.long`): The timestep that determines which transition matrices are used. x_t (`torch.LongTensor` of shape `(batch size, num latent pixels)`): The classes of each latent pixel at time `t`. generator (`torch.Generator`, or `None`): A random number generator for the noise applied to `p(x_{t-1} | x_t)` before it is sampled from. return_dict (`bool`, *optional*, defaults to `True`): Whether or not to return a [`~schedulers.scheduling_vq_diffusion.VQDiffusionSchedulerOutput`] or `tuple`. Returns: [`~schedulers.scheduling_vq_diffusion.VQDiffusionSchedulerOutput`] or `tuple`: If return_dict is `True`, [`~schedulers.scheduling_vq_diffusion.VQDiffusionSchedulerOutput`] is returned, otherwise a tuple is returned where the first element is the sample tensor. """ if timestep == 0: log_p_x_t_min_1 = model_output else: log_p_x_t_min_1 = self.q_posterior(model_output, sample, timestep) log_p_x_t_min_1 = gumbel_noised(log_p_x_t_min_1, generator) x_t_min_1 = log_p_x_t_min_1.argmax(dim=1) if not return_dict: return (x_t_min_1,) return VQDiffusionSchedulerOutput(prev_sample=x_t_min_1) def q_posterior(self, log_p_x_0, x_t, t): """ Calculates the log probabilities for the predicted classes of the image at timestep `t-1`: ``` p(x_{t-1} | x_t) = sum( q(x_t | x_{t-1}) * q(x_{t-1} | x_0) * p(x_0) / q(x_t | x_0) ) ``` Args: log_p_x_0 (`torch.FloatTensor` of shape `(batch size, num classes - 1, num latent pixels)`): The log probabilities for the predicted classes of the initial latent pixels. Does not include a prediction for the masked class as the initial unnoised image cannot be masked. x_t (`torch.LongTensor` of shape `(batch size, num latent pixels)`): The classes of each latent pixel at time `t`. t (`torch.Long`): The timestep that determines which transition matrix is used. Returns: `torch.FloatTensor` of shape `(batch size, num classes, num latent pixels)`: The log probabilities for the predicted classes of the image at timestep `t-1`. """ log_onehot_x_t = index_to_log_onehot(x_t, self.num_embed) log_q_x_t_given_x_0 = self.log_Q_t_transitioning_to_known_class( t=t, x_t=x_t, log_onehot_x_t=log_onehot_x_t, cumulative=True ) log_q_t_given_x_t_min_1 = self.log_Q_t_transitioning_to_known_class( t=t, x_t=x_t, log_onehot_x_t=log_onehot_x_t, cumulative=False ) # p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) ... p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) # . . . # . . . # . . . # p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) ... p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) q = log_p_x_0 - log_q_x_t_given_x_0 # sum_0 = p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) + ... + p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}), ... , # sum_n = p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) + ... + p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) q_log_sum_exp = torch.logsumexp(q, dim=1, keepdim=True) # p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_0 ... p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_n # . . . # . . . # . . . # p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_0 ... p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_n q = q - q_log_sum_exp # (p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1} ... (p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1} # . . . # . . . # . . . # (p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1} ... (p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1} # c_cumulative_{t-1} ... c_cumulative_{t-1} q = self.apply_cumulative_transitions(q, t - 1) # ((p_0(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_0) * sum_0 ... ((p_n(x_0=C_0 | x_t) / q(x_t | x_0=C_0) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_0) * sum_n # . . . # . . . # . . . # ((p_0(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_0) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_{k-1}) * sum_0 ... ((p_n(x_0=C_{k-1} | x_t) / q(x_t | x_0=C_{k-1}) / sum_n) * a_cumulative_{t-1} + b_cumulative_{t-1}) * q(x_t | x_{t-1}=C_{k-1}) * sum_n # c_cumulative_{t-1} * q(x_t | x_{t-1}=C_k) * sum_0 ... c_cumulative_{t-1} * q(x_t | x_{t-1}=C_k) * sum_0 log_p_x_t_min_1 = q + log_q_t_given_x_t_min_1 + q_log_sum_exp # For each column, there are two possible cases. # # Where: # - sum(p_n(x_0))) is summing over all classes for x_0 # - C_i is the class transitioning from (not to be confused with c_t and c_cumulative_t being used for gamma's) # - C_j is the class transitioning to # # 1. x_t is masked i.e. x_t = c_k # # Simplifying the expression, the column vector is: # . # . # . # (c_t / c_cumulative_t) * (a_cumulative_{t-1} * p_n(x_0 = C_i | x_t) + b_cumulative_{t-1} * sum(p_n(x_0))) # . # . # . # (c_cumulative_{t-1} / c_cumulative_t) * sum(p_n(x_0)) # # From equation (11) stated in terms of forward probabilities, the last row is trivially verified. # # For the other rows, we can state the equation as ... # # (c_t / c_cumulative_t) * [b_cumulative_{t-1} * p(x_0=c_0) + ... + (a_cumulative_{t-1} + b_cumulative_{t-1}) * p(x_0=C_i) + ... + b_cumulative_{k-1} * p(x_0=c_{k-1})] # # This verifies the other rows. # # 2. x_t is not masked # # Simplifying the expression, there are two cases for the rows of the column vector, where C_j = C_i and where C_j != C_i: # . # . # . # C_j != C_i: b_t * ((b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_0) + ... + ((a_cumulative_{t-1} + b_cumulative_{t-1}) / b_cumulative_t) * p_n(x_0 = C_i) + ... + (b_cumulative_{t-1} / (a_cumulative_t + b_cumulative_t)) * p_n(c_0=C_j) + ... + (b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_{k-1})) # . # . # . # C_j = C_i: (a_t + b_t) * ((b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_0) + ... + ((a_cumulative_{t-1} + b_cumulative_{t-1}) / (a_cumulative_t + b_cumulative_t)) * p_n(x_0 = C_i = C_j) + ... + (b_cumulative_{t-1} / b_cumulative_t) * p_n(x_0 = c_{k-1})) # . # . # . # 0 # # The last row is trivially verified. The other rows can be verified by directly expanding equation (11) stated in terms of forward probabilities. return log_p_x_t_min_1 def log_Q_t_transitioning_to_known_class( self, *, t: torch.int, x_t: torch.LongTensor, log_onehot_x_t: torch.FloatTensor, cumulative: bool ): """ Calculates the log probabilities of the rows from the (cumulative or non-cumulative) transition matrix for each latent pixel in `x_t`. Args: t (`torch.Long`): The timestep that determines which transition matrix is used. x_t (`torch.LongTensor` of shape `(batch size, num latent pixels)`): The classes of each latent pixel at time `t`. log_onehot_x_t (`torch.FloatTensor` of shape `(batch size, num classes, num latent pixels)`): The log one-hot vectors of `x_t`. cumulative (`bool`): If cumulative is `False`, the single step transition matrix `t-1`->`t` is used. If cumulative is `True`, the cumulative transition matrix `0`->`t` is used. Returns: `torch.FloatTensor` of shape `(batch size, num classes - 1, num latent pixels)`: Each _column_ of the returned matrix is a _row_ of log probabilities of the complete probability transition matrix. When non cumulative, returns `self.num_classes - 1` rows because the initial latent pixel cannot be masked. Where: - `q_n` is the probability distribution for the forward process of the `n`th latent pixel. - C_0 is a class of a latent pixel embedding - C_k is the class of the masked latent pixel non-cumulative result (omitting logarithms): ``` q_0(x_t | x_{t-1} = C_0) ... q_n(x_t | x_{t-1} = C_0) . . . . . . . . . q_0(x_t | x_{t-1} = C_k) ... q_n(x_t | x_{t-1} = C_k) ``` cumulative result (omitting logarithms): ``` q_0_cumulative(x_t | x_0 = C_0) ... q_n_cumulative(x_t | x_0 = C_0) . . . . . . . . . q_0_cumulative(x_t | x_0 = C_{k-1}) ... q_n_cumulative(x_t | x_0 = C_{k-1}) ``` """ if cumulative: a = self.log_cumprod_at[t] b = self.log_cumprod_bt[t] c = self.log_cumprod_ct[t] else: a = self.log_at[t] b = self.log_bt[t] c = self.log_ct[t] if not cumulative: # The values in the onehot vector can also be used as the logprobs for transitioning # from masked latent pixels. If we are not calculating the cumulative transitions, # we need to save these vectors to be re-appended to the final matrix so the values # aren't overwritten. # # `P(x_t!=mask|x_{t-1=mask}) = 0` and 0 will be the value of the last row of the onehot vector # if x_t is not masked # # `P(x_t=mask|x_{t-1=mask}) = 1` and 1 will be the value of the last row of the onehot vector # if x_t is masked log_onehot_x_t_transitioning_from_masked = log_onehot_x_t[:, -1, :].unsqueeze(1) # `index_to_log_onehot` will add onehot vectors for masked pixels, # so the default one hot matrix has one too many rows. See the doc string # for an explanation of the dimensionality of the returned matrix. log_onehot_x_t = log_onehot_x_t[:, :-1, :] # this is a cheeky trick to produce the transition probabilities using log one-hot vectors. # # Don't worry about what values this sets in the columns that mark transitions # to masked latent pixels. They are overwrote later with the `mask_class_mask`. # # Looking at the below logspace formula in non-logspace, each value will evaluate to either # `1 * a + b = a + b` where `log_Q_t` has the one hot value in the column # or # `0 * a + b = b` where `log_Q_t` has the 0 values in the column. # # See equation 7 for more details. log_Q_t = (log_onehot_x_t + a).logaddexp(b) # The whole column of each masked pixel is `c` mask_class_mask = x_t == self.mask_class mask_class_mask = mask_class_mask.unsqueeze(1).expand(-1, self.num_embed - 1, -1) log_Q_t[mask_class_mask] = c if not cumulative: log_Q_t = torch.cat((log_Q_t, log_onehot_x_t_transitioning_from_masked), dim=1) return log_Q_t def apply_cumulative_transitions(self, q, t): bsz = q.shape[0] a = self.log_cumprod_at[t] b = self.log_cumprod_bt[t] c = self.log_cumprod_ct[t] num_latent_pixels = q.shape[2] c = c.expand(bsz, 1, num_latent_pixels) q = (q + a).logaddexp(b) q = torch.cat((q, c), dim=1) return q