Add beta sigmas to other schedulers and update docs (#9538)

Author: hlky

docs/source/en/api/schedulers/overview.md

@@ -52,6 +52,7 @@ Many schedulers are implemented from the [k-diffusion](https://github.com/crowso
 | sgm_uniform              | init with `timestep_spacing="trailing"`                                    |
 | simple                   | init with `timestep_spacing="trailing"`                                    |
 | exponential              | init with `timestep_spacing="linspace"`, `use_exponential_sigmas=True`     |
+| beta                     | init with `timestep_spacing="linspace"`, `use_beta_sigmas=True`            |
 
 All schedulers are built from the base [`SchedulerMixin`] class which implements low level utilities shared by all schedulers.
 

src/diffusers/schedulers/scheduling_deis_multistep.py

@@ -22,10 +22,14 @@
 import torch
 
 from ..configuration_utils import ConfigMixin, register_to_config
-from ..utils import deprecate
+from ..utils import deprecate, is_scipy_available
 from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
 
 
+if is_scipy_available():
+    import scipy.stats
+
+
 # Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
 def betas_for_alpha_bar(
     num_diffusion_timesteps,
@@ -113,6 +117,9 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
              the sigmas are determined according to a sequence of noise levels {σi}.
         use_exponential_sigmas (`bool`, *optional*, defaults to `False`):
             Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
+        use_beta_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
+            Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
         timestep_spacing (`str`, defaults to `"linspace"`):
             The way the timesteps should be scaled. Refer to Table 2 of the [Common Diffusion Noise Schedules and
             Sample Steps are Flawed](https://huggingface.co/papers/2305.08891) for more information.
@@ -141,11 +148,16 @@ def __init__(
         lower_order_final: bool = True,
         use_karras_sigmas: Optional[bool] = False,
         use_exponential_sigmas: Optional[bool] = False,
+        use_beta_sigmas: Optional[bool] = False,
         timestep_spacing: str = "linspace",
         steps_offset: int = 0,
     ):
-        if sum([self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
-            raise ValueError("Only one of `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used.")
+        if self.config.use_beta_sigmas and not is_scipy_available():
+            raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
+        if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
+            raise ValueError(
+                "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
+            )
         if trained_betas is not None:
             self.betas = torch.tensor(trained_betas, dtype=torch.float32)
         elif beta_schedule == "linear":
@@ -263,6 +275,9 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
         elif self.config.use_exponential_sigmas:
             sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
             timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
+        elif self.config.use_beta_sigmas:
+            sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
+            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
         else:
             sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
             sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
@@ -396,6 +411,38 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
         sigmas = torch.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps).exp()
         return sigmas
 
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
+    def _convert_to_beta(
+        self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
+    ) -> torch.Tensor:
+        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        sigmas = torch.Tensor(
+            [
+                sigma_min + (ppf * (sigma_max - sigma_min))
+                for ppf in [
+                    scipy.stats.beta.ppf(timestep, alpha, beta)
+                    for timestep in 1 - np.linspace(0, 1, num_inference_steps)
+                ]
+            ]
+        )
+        return sigmas
+
     def convert_model_output(
         self,
         model_output: torch.Tensor,

src/diffusers/schedulers/scheduling_dpmsolver_multistep.py

@@ -21,11 +21,15 @@
 import torch
 
 from ..configuration_utils import ConfigMixin, register_to_config
-from ..utils import deprecate
+from ..utils import deprecate, is_scipy_available
 from ..utils.torch_utils import randn_tensor
 from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
 
 
+if is_scipy_available():
+    import scipy.stats
+
+
 # Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
 def betas_for_alpha_bar(
     num_diffusion_timesteps,
@@ -163,6 +167,9 @@ class DPMSolverMultistepScheduler(SchedulerMixin, ConfigMixin):
             the sigmas are determined according to a sequence of noise levels {σi}.
         use_exponential_sigmas (`bool`, *optional*, defaults to `False`):
             Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
+        use_beta_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
+            Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
         use_lu_lambdas (`bool`, *optional*, defaults to `False`):
             Whether to use the uniform-logSNR for step sizes proposed by Lu's DPM-Solver in the noise schedule during
             the sampling process. If `True`, the sigmas and time steps are determined according to a sequence of
@@ -209,6 +216,7 @@ def __init__(
         euler_at_final: bool = False,
         use_karras_sigmas: Optional[bool] = False,
         use_exponential_sigmas: Optional[bool] = False,
+        use_beta_sigmas: Optional[bool] = False,
         use_lu_lambdas: Optional[bool] = False,
         final_sigmas_type: Optional[str] = "zero",  # "zero", "sigma_min"
         lambda_min_clipped: float = -float("inf"),
@@ -217,8 +225,12 @@ def __init__(
         steps_offset: int = 0,
         rescale_betas_zero_snr: bool = False,
     ):
-        if sum([self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
-            raise ValueError("Only one of `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used.")
+        if self.config.use_beta_sigmas and not is_scipy_available():
+            raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
+        if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
+            raise ValueError(
+                "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
+            )
         if algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
             deprecation_message = f"algorithm_type {algorithm_type} is deprecated and will be removed in a future version. Choose from `dpmsolver++` or `sde-dpmsolver++` instead"
             deprecate("algorithm_types dpmsolver and sde-dpmsolver", "1.0.0", deprecation_message)
@@ -337,6 +349,8 @@ def set_timesteps(
             raise ValueError("Cannot use `timesteps` with `config.use_lu_lambdas = True`")
         if timesteps is not None and self.config.use_exponential_sigmas:
             raise ValueError("Cannot set `timesteps` with `config.use_exponential_sigmas = True`.")
+        if timesteps is not None and self.config.use_beta_sigmas:
+            raise ValueError("Cannot set `timesteps` with `config.use_beta_sigmas = True`.")
 
         if timesteps is not None:
             timesteps = np.array(timesteps).astype(np.int64)
@@ -388,6 +402,9 @@ def set_timesteps(
         elif self.config.use_exponential_sigmas:
             sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
             timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
+        elif self.config.use_beta_sigmas:
+            sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
+            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
         else:
             sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
 
@@ -542,6 +559,38 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
         sigmas = torch.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps).exp()
         return sigmas
 
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
+    def _convert_to_beta(
+        self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
+    ) -> torch.Tensor:
+        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        sigmas = torch.Tensor(
+            [
+                sigma_min + (ppf * (sigma_max - sigma_min))
+                for ppf in [
+                    scipy.stats.beta.ppf(timestep, alpha, beta)
+                    for timestep in 1 - np.linspace(0, 1, num_inference_steps)
+                ]
+            ]
+        )
+        return sigmas
+
     def convert_model_output(
         self,
         model_output: torch.Tensor,

src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py

@@ -21,11 +21,15 @@
 import torch
 
 from ..configuration_utils import ConfigMixin, register_to_config
-from ..utils import deprecate
+from ..utils import deprecate, is_scipy_available
 from ..utils.torch_utils import randn_tensor
 from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin, SchedulerOutput
 
 
+if is_scipy_available():
+    import scipy.stats
+
+
 # Copied from diffusers.schedulers.scheduling_ddpm.betas_for_alpha_bar
 def betas_for_alpha_bar(
     num_diffusion_timesteps,
@@ -126,6 +130,9 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
             the sigmas are determined according to a sequence of noise levels {σi}.
         use_exponential_sigmas (`bool`, *optional*, defaults to `False`):
             Whether to use exponential sigmas for step sizes in the noise schedule during the sampling process.
+        use_beta_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use beta sigmas for step sizes in the noise schedule during the sampling process. Refer to [Beta
+            Sampling is All You Need](https://huggingface.co/papers/2407.12173) for more information.
         lambda_min_clipped (`float`, defaults to `-inf`):
             Clipping threshold for the minimum value of `lambda(t)` for numerical stability. This is critical for the
             cosine (`squaredcos_cap_v2`) noise schedule.
@@ -161,13 +168,18 @@ def __init__(
         euler_at_final: bool = False,
         use_karras_sigmas: Optional[bool] = False,
         use_exponential_sigmas: Optional[bool] = False,
+        use_beta_sigmas: Optional[bool] = False,
         lambda_min_clipped: float = -float("inf"),
         variance_type: Optional[str] = None,
         timestep_spacing: str = "linspace",
         steps_offset: int = 0,
     ):
-        if sum([self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
-            raise ValueError("Only one of `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used.")
+        if self.config.use_beta_sigmas and not is_scipy_available():
+            raise ImportError("Make sure to install scipy if you want to use beta sigmas.")
+        if sum([self.config.use_beta_sigmas, self.config.use_exponential_sigmas, self.config.use_karras_sigmas]) > 1:
+            raise ValueError(
+                "Only one of `config.use_beta_sigmas`, `config.use_exponential_sigmas`, `config.use_karras_sigmas` can be used."
+            )
         if algorithm_type in ["dpmsolver", "sde-dpmsolver"]:
             deprecation_message = f"algorithm_type {algorithm_type} is deprecated and will be removed in a future version. Choose from `dpmsolver++` or `sde-dpmsolver++` instead"
             deprecate("algorithm_types dpmsolver and sde-dpmsolver", "1.0.0", deprecation_message)
@@ -219,6 +231,7 @@ def __init__(
         self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
         self.use_karras_sigmas = use_karras_sigmas
         self.use_exponential_sigmas = use_exponential_sigmas
+        self.use_beta_sigmas = use_beta_sigmas
 
     @property
     def step_index(self):
@@ -276,6 +289,9 @@ def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torc
         elif self.config.use_exponential_sigmas:
             sigmas = self._convert_to_exponential(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
             timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
+        elif self.config.use_beta_sigmas:
+            sigmas = self._convert_to_beta(in_sigmas=sigmas, num_inference_steps=self.num_inference_steps)
+            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
         else:
             sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
             sigma_max = (
@@ -416,6 +432,38 @@ def _convert_to_exponential(self, in_sigmas: torch.Tensor, num_inference_steps:
         sigmas = torch.linspace(math.log(sigma_max), math.log(sigma_min), num_inference_steps).exp()
         return sigmas
 
+    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_beta
+    def _convert_to_beta(
+        self, in_sigmas: torch.Tensor, num_inference_steps: int, alpha: float = 0.6, beta: float = 0.6
+    ) -> torch.Tensor:
+        """From "Beta Sampling is All You Need" [arXiv:2407.12173] (Lee et. al, 2024)"""
+
+        # Hack to make sure that other schedulers which copy this function don't break
+        # TODO: Add this logic to the other schedulers
+        if hasattr(self.config, "sigma_min"):
+            sigma_min = self.config.sigma_min
+        else:
+            sigma_min = None
+
+        if hasattr(self.config, "sigma_max"):
+            sigma_max = self.config.sigma_max
+        else:
+            sigma_max = None
+
+        sigma_min = sigma_min if sigma_min is not None else in_sigmas[-1].item()
+        sigma_max = sigma_max if sigma_max is not None else in_sigmas[0].item()
+
+        sigmas = torch.Tensor(
+            [
+                sigma_min + (ppf * (sigma_max - sigma_min))
+                for ppf in [
+                    scipy.stats.beta.ppf(timestep, alpha, beta)
+                    for timestep in 1 - np.linspace(0, 1, num_inference_steps)
+                ]
+            ]
+        )
+        return sigmas
+
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.convert_model_output
     def convert_model_output(
         self,