diff --git a/src/diffusers/schedulers/scheduling_deis_multistep.py b/src/diffusers/schedulers/scheduling_deis_multistep.py
index 09ce338a9222..b7d64fc00bae 100644
--- a/src/diffusers/schedulers/scheduling_deis_multistep.py
+++ b/src/diffusers/schedulers/scheduling_deis_multistep.py
@@ -84,33 +84,35 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
     methods the library implements for all schedulers such as loading and saving.
 
     Args:
-        num_train_timesteps (`int`, defaults to 1000):
+        num_train_timesteps (`int`, defaults to `1000`):
             The number of diffusion steps to train the model.
-        beta_start (`float`, defaults to 0.0001):
+        beta_start (`float`, defaults to `0.0001`):
             The starting `beta` value of inference.
-        beta_end (`float`, defaults to 0.02):
+        beta_end (`float`, defaults to `0.02`):
             The final `beta` value.
-        beta_schedule (`str`, defaults to `"linear"`):
+        beta_schedule (`"linear"`, `"scaled_linear"`, or `"squaredcos_cap_v2"`, defaults to `"linear"`):
             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 (`np.ndarray`, *optional*):
+        trained_betas (`np.ndarray` or `List[float]`, *optional*):
             Pass an array of betas directly to the constructor to bypass `beta_start` and `beta_end`.
-        solver_order (`int`, defaults to 2):
+        solver_order (`int`, defaults to `2`):
             The DEIS order which can be `1` or `2` or `3`. It is recommended to use `solver_order=2` for guided
             sampling, and `solver_order=3` for unconditional sampling.
-        prediction_type (`str`, defaults to `epsilon`):
+        prediction_type (`"epsilon"`, `"sample"`, `"v_prediction"`, or `"flow_prediction"`, defaults to `"epsilon"`):
             Prediction type of the scheduler function; can be `epsilon` (predicts the noise of the diffusion process),
-            `sample` (directly predicts the noisy sample`) or `v_prediction` (see section 2.4 of [Imagen
-            Video](https://huggingface.co/papers/2210.02303) paper).
+            `sample` (directly predicts the noisy sample`), `v_prediction` (see section 2.4 of [Imagen
+            Video](https://huggingface.co/papers/2210.02303) paper), or `flow_prediction`.
         thresholding (`bool`, defaults to `False`):
             Whether to use the "dynamic thresholding" method. This is unsuitable for latent-space diffusion models such
             as Stable Diffusion.
-        dynamic_thresholding_ratio (`float`, defaults to 0.995):
+        dynamic_thresholding_ratio (`float`, defaults to `0.995`):
             The ratio for the dynamic thresholding method. Valid only when `thresholding=True`.
-        sample_max_value (`float`, defaults to 1.0):
+        sample_max_value (`float`, defaults to `1.0`):
             The threshold value for dynamic thresholding. Valid only when `thresholding=True`.
-        algorithm_type (`str`, defaults to `deis`):
+        algorithm_type (`"deis"`, defaults to `"deis"`):
             The algorithm type for the solver.
+        solver_type (`"logrho"`, defaults to `"logrho"`):
+            Solver type for DEIS.
         lower_order_final (`bool`, defaults to `True`):
             Whether to use lower-order solvers in the final steps. Only valid for < 15 inference steps.
         use_karras_sigmas (`bool`, *optional*, defaults to `False`):
@@ -121,11 +123,19 @@ class DEISMultistepScheduler(SchedulerMixin, ConfigMixin):
         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"`):
+        use_flow_sigmas (`bool`, *optional*, defaults to `False`):
+            Whether to use flow sigmas for step sizes in the noise schedule during the sampling process.
+        flow_shift (`float`, *optional*, defaults to `1.0`):
+            The flow shift parameter for flow-based models.
+        timestep_spacing (`"linspace"`, `"leading"`, or `"trailing"`, 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.
-        steps_offset (`int`, defaults to 0):
+        steps_offset (`int`, defaults to `0`):
             An offset added to the inference steps, as required by some model families.
+        use_dynamic_shifting (`bool`, defaults to `False`):
+            Whether to use dynamic shifting for the noise schedule.
+        time_shift_type (`"exponential"`, defaults to `"exponential"`):
+            The type of time shifting to apply.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -137,29 +147,38 @@ def __init__(
         num_train_timesteps: int = 1000,
         beta_start: float = 0.0001,
         beta_end: float = 0.02,
-        beta_schedule: str = "linear",
-        trained_betas: Optional[np.ndarray] = None,
+        beta_schedule: Literal["linear", "scaled_linear", "squaredcos_cap_v2"] = "linear",
+        trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
         solver_order: int = 2,
-        prediction_type: str = "epsilon",
+        prediction_type: Literal["epsilon", "sample", "v_prediction", "flow_prediction"] = "epsilon",
         thresholding: bool = False,
         dynamic_thresholding_ratio: float = 0.995,
         sample_max_value: float = 1.0,
-        algorithm_type: str = "deis",
-        solver_type: str = "logrho",
+        algorithm_type: Literal["deis"] = "deis",
+        solver_type: Literal["logrho"] = "logrho",
         lower_order_final: bool = True,
         use_karras_sigmas: Optional[bool] = False,
         use_exponential_sigmas: Optional[bool] = False,
         use_beta_sigmas: Optional[bool] = False,
         use_flow_sigmas: Optional[bool] = False,
         flow_shift: Optional[float] = 1.0,
-        timestep_spacing: str = "linspace",
+        timestep_spacing: Literal["linspace", "leading", "trailing"] = "linspace",
         steps_offset: int = 0,
         use_dynamic_shifting: bool = False,
-        time_shift_type: str = "exponential",
-    ):
+        time_shift_type: Literal["exponential"] = "exponential",
+    ) -> None:
         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:
+        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."
             )
@@ -169,7 +188,15 @@ def __init__(
             self.betas = torch.linspace(beta_start, beta_end, num_train_timesteps, dtype=torch.float32)
         elif beta_schedule == "scaled_linear":
             # this schedule is very specific to the latent diffusion model.
-            self.betas = torch.linspace(beta_start**0.5, beta_end**0.5, num_train_timesteps, dtype=torch.float32) ** 2
+            self.betas = (
+                torch.linspace(
+                    beta_start**0.5,
+                    beta_end**0.5,
+                    num_train_timesteps,
+                    dtype=torch.float32,
+                )
+                ** 2
+            )
         elif beta_schedule == "squaredcos_cap_v2":
             # Glide cosine schedule
             self.betas = betas_for_alpha_bar(num_train_timesteps)
@@ -211,21 +238,21 @@ def __init__(
         self.sigmas = self.sigmas.to("cpu")  # to avoid too much CPU/GPU communication
 
     @property
-    def step_index(self):
+    def step_index(self) -> Optional[int]:
         """
         The index counter for current timestep. It will increase 1 after each scheduler step.
         """
         return self._step_index
 
     @property
-    def begin_index(self):
+    def begin_index(self) -> Optional[int]:
         """
         The index for the first timestep. It should be set from pipeline with `set_begin_index` method.
         """
         return self._begin_index
 
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.set_begin_index
-    def set_begin_index(self, begin_index: int = 0):
+    def set_begin_index(self, begin_index: int = 0) -> None:
         """
         Sets the begin index for the scheduler. This function should be run from pipeline before the inference.
 
@@ -236,8 +263,11 @@ def set_begin_index(self, begin_index: int = 0):
         self._begin_index = begin_index
 
     def set_timesteps(
-        self, num_inference_steps: int, device: Union[str, torch.device] = None, mu: Optional[float] = None
-    ):
+        self,
+        num_inference_steps: int,
+        device: Union[str, torch.device] = None,
+        mu: Optional[float] = None,
+    ) -> None:
         """
         Sets the discrete timesteps used for the diffusion chain (to be run before inference).
 
@@ -246,6 +276,9 @@ def set_timesteps(
                 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 should be moved to. If `None`, the timesteps are not moved.
+            mu (`float`, *optional*):
+                The mu parameter for dynamic shifting. Only used when `use_dynamic_shifting=True` and
+                `time_shift_type="exponential"`.
         """
         if mu is not None:
             assert self.config.use_dynamic_shifting and self.config.time_shift_type == "exponential"
@@ -363,7 +396,7 @@ def _threshold_sample(self, sample: torch.Tensor) -> torch.Tensor:
         return sample
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._sigma_to_t
-    def _sigma_to_t(self, sigma, log_sigmas):
+    def _sigma_to_t(self, sigma: np.ndarray, log_sigmas: np.ndarray) -> np.ndarray:
         """
         Convert sigma values to corresponding timestep values through interpolation.
 
@@ -400,7 +433,7 @@ def _sigma_to_t(self, sigma, log_sigmas):
         return t
 
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._sigma_to_alpha_sigma_t
-    def _sigma_to_alpha_sigma_t(self, sigma):
+    def _sigma_to_alpha_sigma_t(self, sigma: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
         """
         Convert sigma values to alpha_t and sigma_t values.
 
@@ -422,7 +455,7 @@ def _sigma_to_alpha_sigma_t(self, sigma):
         return alpha_t, sigma_t
 
     # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler._convert_to_karras
-    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps) -> torch.Tensor:
+    def _convert_to_karras(self, in_sigmas: torch.Tensor, num_inference_steps: int) -> torch.Tensor:
         """
         Construct the noise schedule as proposed in [Elucidating the Design Space of Diffusion-Based Generative
         Models](https://huggingface.co/papers/2206.00364).
@@ -648,7 +681,10 @@ def deis_first_order_update(
                 "Passing `prev_timestep` is deprecated and has no effect as model output conversion is now handled via an internal counter `self.step_index`",
             )
 
-        sigma_t, sigma_s = self.sigmas[self.step_index + 1], self.sigmas[self.step_index]
+        sigma_t, sigma_s = (
+            self.sigmas[self.step_index + 1],
+            self.sigmas[self.step_index],
+        )
         alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma_t)
         alpha_s, sigma_s = self._sigma_to_alpha_sigma_t(sigma_s)
         lambda_t = torch.log(alpha_t) - torch.log(sigma_t)
@@ -714,7 +750,11 @@ def multistep_deis_second_order_update(
 
         m0, m1 = model_output_list[-1], model_output_list[-2]
 
-        rho_t, rho_s0, rho_s1 = sigma_t / alpha_t, sigma_s0 / alpha_s0, sigma_s1 / alpha_s1
+        rho_t, rho_s0, rho_s1 = (
+            sigma_t / alpha_t,
+            sigma_s0 / alpha_s0,
+            sigma_s1 / alpha_s1,
+        )
 
         if self.config.algorithm_type == "deis":
 
@@ -854,7 +894,7 @@ def index_for_timestep(
         return step_index
 
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler._init_step_index
-    def _init_step_index(self, timestep):
+    def _init_step_index(self, timestep: Union[int, torch.Tensor]) -> None:
         """
         Initialize the step_index counter for the scheduler.
 
@@ -884,18 +924,17 @@ def step(
         Args:
             model_output (`torch.Tensor`):
                 The direct output from learned diffusion model.
-            timestep (`int`):
+            timestep (`int` or `torch.Tensor`):
                 The current discrete timestep in the diffusion chain.
             sample (`torch.Tensor`):
                 A current instance of a sample created by the diffusion process.
-            return_dict (`bool`):
+            return_dict (`bool`, defaults to `True`):
                 Whether or not to return a [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`.
 
         Returns:
             [`~schedulers.scheduling_utils.SchedulerOutput`] or `tuple`:
                 If return_dict is `True`, [`~schedulers.scheduling_utils.SchedulerOutput`] is returned, otherwise a
                 tuple is returned where the first element is the sample tensor.
-
         """
         if self.num_inference_steps is None:
             raise ValueError(
@@ -1000,5 +1039,5 @@ def add_noise(
         noisy_samples = alpha_t * original_samples + sigma_t * noise
         return noisy_samples
 
-    def __len__(self):
+    def __len__(self) -> int:
         return self.config.num_train_timesteps