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| # 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 | |
| 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 | |
| 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 | |