Karras VE, DDIM and DDPM flax schedulers

examples/textual_inversion/textual_inversion.py

@@ -504,7 +504,9 @@ def main():
                 noise = torch.randn(latents.shape).to(latents.device)
                 bsz = latents.shape[0]
                 # Sample a random timestep for each image
-                timesteps = torch.randint(0, noise_scheduler.num_train_timesteps, (bsz,), device=latents.device).long()
+                timesteps = torch.randint(
+                    0, noise_scheduler.config.num_train_timesteps, (bsz,), device=latents.device
+                ).long()
 
                 # Add noise to the latents according to the noise magnitude at each timestep
                 # (this is the forward diffusion process)

examples/unconditional_image_generation/train_unconditional.py

@@ -130,7 +130,7 @@ def transforms(examples):
             bsz = clean_images.shape[0]
             # Sample a random timestep for each image
             timesteps = torch.randint(
-                0, noise_scheduler.num_train_timesteps, (bsz,), device=clean_images.device
+                0, noise_scheduler.config.num_train_timesteps, (bsz,), device=clean_images.device
             ).long()
 
             # Add noise to the clean images according to the noise magnitude at each timestep

src/diffusers/__init__.py

@@ -64,6 +64,13 @@
 
 if is_flax_available():
     from .modeling_flax_utils import FlaxModelMixin
-    from .schedulers import FlaxPNDMScheduler
+    from .schedulers import (
+        FlaxDDIMScheduler,
+        FlaxDDPMScheduler,
+        FlaxKarrasVeScheduler,
+        FlaxLMSDiscreteScheduler,
+        FlaxPNDMScheduler,
+        FlaxScoreSdeVeScheduler,
+    )
 else:
     from .utils.dummy_flax_objects import *  # noqa F403

src/diffusers/modeling_flax_utils.py

@@ -386,7 +386,7 @@ def from_pretrained(
                         raise ValueError from e
             except (UnicodeDecodeError, ValueError):
                 raise EnvironmentError(f"Unable to convert {model_file} to Flax deserializable object. ")
-        # make sure all arrays are stored as jnp.arrays
+        # make sure all arrays are stored as jnp.ndarray
         # NOTE: This is to prevent a bug this will be fixed in Flax >= v0.3.4:
         # https://github.com/google/flax/issues/1261
         state = jax.tree_util.tree_map(lambda x: jax.device_put(x, jax.devices("cpu")[0]), state)

src/diffusers/pipelines/score_sde_ve/pipeline_score_sde_ve.py

@@ -80,7 +80,7 @@ def __call__(
             sigma_t = self.scheduler.sigmas[i] * torch.ones(shape[0], device=self.device)
 
             # correction step
-            for _ in range(self.scheduler.correct_steps):
+            for _ in range(self.scheduler.config.correct_steps):
                 model_output = self.unet(sample, sigma_t).sample
                 sample = self.scheduler.step_correct(model_output, sample, generator=generator).prev_sample
 

src/diffusers/schedulers/__init__.py

@@ -28,7 +28,12 @@
     from ..utils.dummy_pt_objects import *  # noqa F403
 
 if is_flax_available():
+    from .scheduling_ddim_flax import FlaxDDIMScheduler
+    from .scheduling_ddpm_flax import FlaxDDPMScheduler
+    from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
+    from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
     from .scheduling_pndm_flax import FlaxPNDMScheduler
+    from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
 else:
     from ..utils.dummy_flax_objects import *  # noqa F403
 

src/diffusers/schedulers/scheduling_ddim.py

@@ -113,7 +113,7 @@ def __init__(
 
         # At every step in ddim, we are looking into the previous alphas_cumprod
         # For the final step, there is no previous alphas_cumprod because we are already at 0
-        # `set_alpha_to_one` decides whether we set this paratemer simply to one or
+        # `set_alpha_to_one` decides whether we set this parameter simply to one or
         # whether we use the final alpha of the "non-previous" one.
         self.final_alpha_cumprod = np.array(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
 
@@ -195,7 +195,7 @@ def step(
         # - pred_original_sample -> f_theta(x_t, t) or x_0
         # - std_dev_t -> sigma_t
         # - eta -> η
-        # - pred_sample_direction -> "direction pointingc to x_t"
+        # - pred_sample_direction -> "direction pointing to x_t"
         # - pred_prev_sample -> "x_t-1"
 
         # 1. get previous step value (=t-1)

src/diffusers/schedulers/scheduling_ddim_flax.py

@@ -0,0 +1,274 @@
+# Copyright 2022 Stanford University Team 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.
+
+# DISCLAIMER: This code is strongly influenced by https://github.com/pesser/pytorch_diffusion
+# and https://github.com/hojonathanho/diffusion
+
+import math
+from dataclasses import dataclass
+from typing import Optional, Tuple, Union
+
+import flax
+import jax.numpy as jnp
+from jax import random
+
+from ..configuration_utils import ConfigMixin, register_to_config
+from .scheduling_utils import SchedulerMixin, SchedulerOutput
+
+
+def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999) -> jnp.ndarray:
+    """
+    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].
+
+    Contains a function alpha_bar that takes an argument t and transforms it to the cumulative product of (1-beta) up
+    to that part of the diffusion process.
+
+
+    Args:
+        num_diffusion_timesteps (`int`): the number of betas to produce.
+        max_beta (`float`): the maximum beta to use; use values lower than 1 to
+                     prevent singularities.
+
+    Returns:
+        betas (`jnp.ndarray`): the betas used by the scheduler to step the model outputs
+    """
+
+    def alpha_bar(time_step):
+        return math.cos((time_step + 0.008) / 1.008 * math.pi / 2) ** 2
+
+    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 jnp.array(betas, dtype=jnp.float32)
+
+
+@flax.struct.dataclass
+class DDIMSchedulerState:
+    # setable values
+    timesteps: jnp.ndarray
+    num_inference_steps: Optional[int] = None
+
+    @classmethod
+    def create(cls, num_train_timesteps: int):
+        return cls(timesteps=jnp.arange(0, num_train_timesteps)[::-1])
+
+
+@dataclass
+class FlaxSchedulerOutput(SchedulerOutput):
+    state: DDIMSchedulerState
+
+
+class FlaxDDIMScheduler(SchedulerMixin, ConfigMixin):
+    """
+    Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising
+    diffusion probabilistic models (DDPMs) with non-Markovian guidance.
+
+    [`~ConfigMixin`] takes care of storing all config attributes that are passed in the scheduler's `__init__`
+    function, such as `num_train_timesteps`. They can be accessed via `scheduler.config.num_train_timesteps`.
+    [`~ConfigMixin`] also provides general loading and saving functionality via the [`~ConfigMixin.save_config`] and
+    [`~ConfigMixin.from_config`] functions.
+
+    For more details, see the original paper: https://arxiv.org/abs/2010.02502
+
+    Args:
+        num_train_timesteps (`int`): number of diffusion steps used to train the model.
+        beta_start (`float`): the starting `beta` value of inference.
+        beta_end (`float`): the final `beta` value.
+        beta_schedule (`str`):
+            the beta schedule, a mapping from a beta range to a sequence of betas for stepping the model. Choose from
+            `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
+        trained_betas (`jnp.ndarray`, optional):
+            option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
+        clip_sample (`bool`, default `True`):
+            option to clip predicted sample between -1 and 1 for numerical stability.
+        set_alpha_to_one (`bool`, default `True`):
+            if alpha for final step is 1 or the final alpha of the "non-previous" one.
+    """
+
+    @register_to_config
+    def __init__(
+        self,
+        num_train_timesteps: int = 1000,
+        beta_start: float = 0.0001,
+        beta_end: float = 0.02,
+        beta_schedule: str = "linear",
+        trained_betas: Optional[jnp.ndarray] = None,
+        clip_sample: bool = True,
+        set_alpha_to_one: bool = True,
+    ):
+        if trained_betas is not None:
+            self.betas = jnp.asarray(trained_betas)
+        if beta_schedule == "linear":
+            self.betas = jnp.linspace(beta_start, beta_end, num_train_timesteps, dtype=jnp.float32)
+        elif beta_schedule == "scaled_linear":
+            # this schedule is very specific to the latent diffusion model.
+            self.betas = jnp.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=jnp.float32) ** 2
+        elif beta_schedule == "squaredcos_cap_v2":
+            # Glide cosine schedule
+            self.betas = betas_for_alpha_bar(num_train_timesteps)
+        else:
+            raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
+
+        self.alphas = 1.0 - self.betas
+        self.alphas_cumprod = jnp.cumprod(self.alphas, axis=0)
+
+        # At every step in ddim, we are looking into the previous alphas_cumprod
+        # For the final step, there is no previous alphas_cumprod because we are already at 0
+        # `set_alpha_to_one` decides whether we set this parameter simply to one or
+        # whether we use the final alpha of the "non-previous" one.
+        self.final_alpha_cumprod = jnp.array(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
+
+        self.state = DDIMSchedulerState.create(num_train_timesteps=num_train_timesteps)
+
+    def _get_variance(self, timestep, prev_timestep):
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
+        beta_prod_t = 1 - alpha_prod_t
+        beta_prod_t_prev = 1 - alpha_prod_t_prev
+
+        variance = (beta_prod_t_prev / beta_prod_t) * (1 - alpha_prod_t / alpha_prod_t_prev)
+
+        return variance
+
+    def set_timesteps(
+        self, state: DDIMSchedulerState, num_inference_steps: int, offset: int = 0
+    ) -> DDIMSchedulerState:
+        """
+        Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
+
+        Args:
+            state (`DDIMSchedulerState`):
+                the `FlaxDDIMScheduler` state data class instance.
+            num_inference_steps (`int`):
+                the number of diffusion steps used when generating samples with a pre-trained model.
+            offset (`int`):
+                optional value to shift timestep values up by. A value of 1 is used in stable diffusion for inference.
+        """
+        step_ratio = self.config.num_train_timesteps // num_inference_steps
+        # creates integer timesteps by multiplying by ratio
+        # casting to int to avoid issues when num_inference_step is power of 3
+        timesteps = (jnp.arange(0, num_inference_steps) * step_ratio).round()[::-1]
+        timesteps = timesteps + offset
+
+        return state.replace(num_inference_steps=num_inference_steps, timesteps=timesteps)
+
+    def step(
+        self,
+        state: DDIMSchedulerState,
+        model_output: jnp.ndarray,
+        timestep: int,
+        sample: jnp.ndarray,
+        key: random.KeyArray,
+        eta: float = 0.0,
+        use_clipped_model_output: bool = False,
+        return_dict: bool = True,
+    ) -> Union[FlaxSchedulerOutput, Tuple]:
+        """
+        Predict the sample at the previous timestep by reversing the SDE. Core function to propagate the diffusion
+        process from the learned model outputs (most often the predicted noise).
+
+        Args:
+            state (`DDIMSchedulerState`): the `FlaxDDIMScheduler` state data class instance.
+            model_output (`jnp.ndarray`): direct output from learned diffusion model.
+            timestep (`int`): current discrete timestep in the diffusion chain.
+            sample (`jnp.ndarray`):
+                current instance of sample being created by diffusion process.
+            key (`random.KeyArray`): a PRNG key.
+            eta (`float`): weight of noise for added noise in diffusion step.
+            use_clipped_model_output (`bool`): TODO
+            return_dict (`bool`): option for returning tuple rather than SchedulerOutput class
+
+        Returns:
+            [`FlaxSchedulerOutput`] or `tuple`: [`FlaxSchedulerOutput`] if `return_dict` is True, otherwise a `tuple`.
+            When returning a tuple, the first element is the sample tensor.
+
+        """
+        if state.num_inference_steps is None:
+            raise ValueError(
+                "Number of inference steps is 'None', you need to run 'set_timesteps' after creating the scheduler"
+            )
+
+        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
+        # Ideally, read DDIM paper in-detail understanding
+
+        # Notation (<variable name> -> <name in paper>
+        # - pred_noise_t -> e_theta(x_t, t)
+        # - pred_original_sample -> f_theta(x_t, t) or x_0
+        # - std_dev_t -> sigma_t
+        # - eta -> η
+        # - pred_sample_direction -> "direction pointing to x_t"
+        # - pred_prev_sample -> "x_t-1"
+
+        # 1. get previous step value (=t-1)
+        prev_timestep = timestep - self.config.num_train_timesteps // state.num_inference_steps
+
+        # 2. compute alphas, betas
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
+        beta_prod_t = 1 - alpha_prod_t
+
+        # 3. compute predicted original sample from predicted noise also called
+        # "predicted x_0" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
+        pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
+
+        # 4. Clip "predicted x_0"
+        if self.config.clip_sample:
+            pred_original_sample = jnp.clip(pred_original_sample, -1, 1)
+
+        # 5. compute variance: "sigma_t(η)" -> see formula (16)
+        # σ_t = sqrt((1 − α_t−1)/(1 − α_t)) * sqrt(1 − α_t/α_t−1)
+        variance = self._get_variance(timestep, prev_timestep)
+        std_dev_t = eta * variance ** (0.5)
+
+        if use_clipped_model_output:
+            # the model_output is always re-derived from the clipped x_0 in Glide
+            model_output = (sample - alpha_prod_t ** (0.5) * pred_original_sample) / beta_prod_t ** (0.5)
+
+        # 6. compute "direction pointing to x_t" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
+        pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * model_output
+
+        # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
+        prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
+
+        if eta > 0:
+            key = random.split(key, num=1)
+            noise = random.normal(key=key, shape=model_output.shape)
+            variance = self._get_variance(timestep, prev_timestep) ** (0.5) * eta * noise
+
+            prev_sample = prev_sample + variance
+
+        if not return_dict:
+            return (prev_sample, state)
+
+        return FlaxSchedulerOutput(prev_sample=prev_sample, state=state)
+
+    def add_noise(
+        self,
+        original_samples: jnp.ndarray,
+        noise: jnp.ndarray,
+        timesteps: jnp.ndarray,
+    ) -> jnp.ndarray:
+        sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
+        sqrt_alpha_prod = self.match_shape(sqrt_alpha_prod, original_samples)
+        sqrt_one_minus_alpha_prod = (1 - self.alphas_cumprod[timesteps]) ** 0.5
+        sqrt_one_minus_alpha_prod = self.match_shape(sqrt_one_minus_alpha_prod, original_samples)
+
+        noisy_samples = sqrt_alpha_prod * original_samples + sqrt_one_minus_alpha_prod * noise
+        return noisy_samples
+
+    def __len__(self):
+        return self.config.num_train_timesteps

src/diffusers/schedulers/scheduling_ddpm.py

@@ -148,7 +148,7 @@ def _get_variance(self, t, predicted_variance=None, variance_type=None):
         if variance_type is None:
             variance_type = self.config.variance_type
 
-        # hacks - were probs added for training stability
+        # hacks - were probably added for training stability
         if variance_type == "fixed_small":
             variance = self.clip(variance, min_value=1e-20)
         # for rl-diffuser https://arxiv.org/abs/2205.09991
@@ -187,7 +187,6 @@ def step(
             timestep (`int`): current discrete timestep in the diffusion chain.
             sample (`torch.FloatTensor` or `np.ndarray`):
                 current instance of sample being created by diffusion process.
-            eta (`float`): weight of noise for added noise in diffusion step.
             predict_epsilon (`bool`):
                 optional flag to use when model predicts the samples directly instead of the noise, epsilon.
             generator: random number generator.