diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_diffedit.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_diffedit.py
index f9bb8d0af4..b2d5953808 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_diffedit.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_diffedit.py
@@ -992,7 +992,7 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
         )
 
         # 4. Preprocess image
-        image = preprocess(image).repeat_interleave(num_maps_per_mask, dim=0)
+        image = self.image_processor.preprocess(image).repeat_interleave(num_maps_per_mask, dim=0)
 
         # 5. Set timesteps
         self.scheduler.set_timesteps(num_inference_steps, device=device)
@@ -1176,7 +1176,7 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
         do_classifier_free_guidance = guidance_scale > 1.0
 
         # 3. Preprocess image
-        image = preprocess(image)
+        image = self.image_processor.preprocess(image)
 
         # 4. Prepare latent variables
         num_images_per_prompt = 1
@@ -1201,9 +1201,9 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
 
         # 7. Noising loop where we obtain the intermediate noised latent image for each timestep.
         num_warmup_steps = len(timesteps) - num_inference_steps * self.inverse_scheduler.order
-        inverted_latents = [latents.detach().clone()]
-        with self.progress_bar(total=num_inference_steps - 1) as progress_bar:
-            for i, t in enumerate(timesteps[:-1]):
+        inverted_latents = []
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.inverse_scheduler.scale_model_input(latent_model_input, t)
@@ -1270,7 +1270,7 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
         # 8. Post-processing
         image = None
         if decode_latents:
-            image = self.decode_latents(latents.flatten(0, 1).detach())
+            image = self.decode_latents(latents.flatten(0, 1))
 
         # 9. Convert to PIL.
         if decode_latents and output_type == "pil":
@@ -1291,7 +1291,7 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
         self,
         prompt: Optional[Union[str, List[str]]] = None,
         mask_image: Union[torch.FloatTensor, PIL.Image.Image] = None,
-        image_latents: torch.FloatTensor = None,
+        image_latents: Union[torch.FloatTensor, PIL.Image.Image] = None,
         inpaint_strength: Optional[float] = 0.8,
         num_inference_steps: int = 50,
         guidance_scale: float = 7.5,
@@ -1447,7 +1447,13 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
         timesteps, num_inference_steps = self.get_timesteps(num_inference_steps, inpaint_strength, device)
 
         # 6. Preprocess image latents
-        image_latents = preprocess(image_latents)
+        if isinstance(image_latents, list) and any(isinstance(l, torch.Tensor) and l.ndim == 5 for l in image_latents):
+            image_latents = torch.cat(image_latents).detach()
+        elif isinstance(image_latents, torch.Tensor) and image_latents.ndim == 5:
+            image_latents = image_latents.detach()
+        else:
+            image_latents = self.image_processor.preprocess(image_latents).detach()
+
         latent_shape = (self.vae.config.latent_channels, latent_height, latent_width)
         if image_latents.shape[-3:] != latent_shape:
             raise ValueError(
@@ -1458,8 +1464,9 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
             image_latents = image_latents.reshape(batch_size, len(timesteps), *latent_shape)
         if image_latents.shape[:2] != (batch_size, len(timesteps)):
             raise ValueError(
-                f"`image_latents` must have batch size {batch_size} with latent images from {len(timesteps)} timesteps, "
-                f"but has batch size {image_latents.shape[0]} with latent images from {image_latents.shape[1]} timesteps."
+                f"`image_latents` must have batch size {batch_size} with latent images from {len(timesteps)}"
+                f" timesteps, but has batch size {image_latents.shape[0]} with latent images from"
+                f" {image_latents.shape[1]} timesteps."
             )
         image_latents = image_latents.transpose(0, 1).repeat_interleave(num_images_per_prompt, dim=1)
         image_latents = image_latents.to(device=device, dtype=prompt_embeds.dtype)
@@ -1468,7 +1475,7 @@ class StableDiffusionDiffEditPipeline(DiffusionPipeline, TextualInversionLoaderM
         extra_step_kwargs = self.prepare_extra_step_kwargs(generator, eta)
 
         # 8. Denoising loop
-        latents = image_latents[0].detach().clone()
+        latents = image_latents[0].clone()
         num_warmup_steps = len(timesteps) - num_inference_steps * self.scheduler.order
         with self.progress_bar(total=num_inference_steps) as progress_bar:
             for i, t in enumerate(timesteps):
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_pix2pix_zero.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_pix2pix_zero.py
index 902bcdd049..960c4369e4 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_pix2pix_zero.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_pix2pix_zero.py
@@ -1183,8 +1183,8 @@ class StableDiffusionPix2PixZeroPipeline(DiffusionPipeline):
 
         # 7. Denoising loop where we obtain the cross-attention maps.
         num_warmup_steps = len(timesteps) - num_inference_steps * self.inverse_scheduler.order
-        with self.progress_bar(total=num_inference_steps - 1) as progress_bar:
-            for i, t in enumerate(timesteps[:-1]):
+        with self.progress_bar(total=num_inference_steps) as progress_bar:
+            for i, t in enumerate(timesteps):
                 # expand the latents if we are doing classifier free guidance
                 latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
                 latent_model_input = self.inverse_scheduler.scale_model_input(latent_model_input, t)
diff --git a/src/diffusers/schedulers/scheduling_ddim_inverse.py b/src/diffusers/schedulers/scheduling_ddim_inverse.py
index c04aabe035..9db83eb992 100644
--- a/src/diffusers/schedulers/scheduling_ddim_inverse.py
+++ b/src/diffusers/schedulers/scheduling_ddim_inverse.py
@@ -90,6 +90,43 @@ def betas_for_alpha_bar(
     return torch.tensor(betas, dtype=torch.float32)
 
 
+# Copied from diffusers.schedulers.scheduling_ddim.rescale_zero_terminal_snr
+def rescale_zero_terminal_snr(betas):
+    """
+    Rescales betas to have zero terminal SNR Based on https://arxiv.org/pdf/2305.08891.pdf (Algorithm 1)
+
+
+    Args:
+        betas (`torch.FloatTensor`):
+            the betas that the scheduler is being initialized with.
+
+    Returns:
+        `torch.FloatTensor`: rescaled betas with zero terminal SNR
+    """
+    # Convert betas to alphas_bar_sqrt
+    alphas = 1.0 - betas
+    alphas_cumprod = torch.cumprod(alphas, dim=0)
+    alphas_bar_sqrt = alphas_cumprod.sqrt()
+
+    # Store old values.
+    alphas_bar_sqrt_0 = alphas_bar_sqrt[0].clone()
+    alphas_bar_sqrt_T = alphas_bar_sqrt[-1].clone()
+
+    # Shift so the last timestep is zero.
+    alphas_bar_sqrt -= alphas_bar_sqrt_T
+
+    # Scale so the first timestep is back to the old value.
+    alphas_bar_sqrt *= alphas_bar_sqrt_0 / (alphas_bar_sqrt_0 - alphas_bar_sqrt_T)
+
+    # Convert alphas_bar_sqrt to betas
+    alphas_bar = alphas_bar_sqrt**2  # Revert sqrt
+    alphas = alphas_bar[1:] / alphas_bar[:-1]  # Revert cumprod
+    alphas = torch.cat([alphas_bar[0:1], alphas])
+    betas = 1 - alphas
+
+    return betas
+
+
 class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
     """
     DDIMInverseScheduler is the reverse scheduler of [`DDIMScheduler`].
@@ -126,9 +163,19 @@ class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
             prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
             process), `sample` (directly predicting the noisy sample`) or `v_prediction` (see section 2.4
             https://imagen.research.google/video/paper.pdf)
+        timestep_spacing (`str`, default `"leading"`):
+            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
+            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
+        rescale_betas_zero_snr (`bool`, default `False`):
+            whether to rescale the betas to have zero terminal SNR (proposed by https://arxiv.org/pdf/2305.08891.pdf).
+            This can enable the model to generate very bright and dark samples instead of limiting it to samples with
+            medium brightness. Loosely related to
+            [`--offset_noise`](https://github.com/huggingface/diffusers/blob/74fd735eb073eb1d774b1ab4154a0876eb82f055/examples/dreambooth/train_dreambooth.py#L506).
     """
 
     order = 1
+    ignore_for_config = ["kwargs"]
+    _deprecated_kwargs = ["set_alpha_to_zero"]
 
     @register_to_config
     def __init__(
@@ -139,18 +186,20 @@ class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
         beta_schedule: str = "linear",
         trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
         clip_sample: bool = True,
-        set_alpha_to_zero: bool = True,
+        set_alpha_to_one: bool = True,
         steps_offset: int = 0,
         prediction_type: str = "epsilon",
         clip_sample_range: float = 1.0,
+        timestep_spacing: str = "leading",
+        rescale_betas_zero_snr: bool = False,
         **kwargs,
     ):
-        if kwargs.get("set_alpha_to_one", None) is not None:
+        if kwargs.get("set_alpha_to_zero", None) is not None:
             deprecation_message = (
-                "The `set_alpha_to_one` argument is deprecated. Please use `set_alpha_to_zero` instead."
+                "The `set_alpha_to_zero` argument is deprecated. Please use `set_alpha_to_one` instead."
             )
-            deprecate("set_alpha_to_one", "1.0.0", deprecation_message, standard_warn=False)
-            set_alpha_to_zero = kwargs["set_alpha_to_one"]
+            deprecate("set_alpha_to_zero", "1.0.0", deprecation_message, standard_warn=False)
+            set_alpha_to_one = kwargs["set_alpha_to_zero"]
         if trained_betas is not None:
             self.betas = torch.tensor(trained_betas, dtype=torch.float32)
         elif beta_schedule == "linear":
@@ -166,15 +215,19 @@ class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
         else:
             raise NotImplementedError(f"{beta_schedule} does is not implemented for {self.__class__}")
 
+        # Rescale for zero SNR
+        if rescale_betas_zero_snr:
+            self.betas = rescale_zero_terminal_snr(self.betas)
+
         self.alphas = 1.0 - self.betas
         self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
 
         # At every step in inverted ddim, we are looking into the next alphas_cumprod
-        # For the final step, there is no next alphas_cumprod, and the index is out of bounds
-        # `set_alpha_to_zero` decides whether we set this parameter simply to zero
+        # For the initial step, there is no current alphas_cumprod, and the index is out of bounds
+        # `set_alpha_to_one` decides whether we set this parameter simply to one
         # in this case, self.step() just output the predicted noise
-        # or whether we use the final alpha of the "non-previous" one.
-        self.final_alpha_cumprod = torch.tensor(0.0) if set_alpha_to_zero else self.alphas_cumprod[-1]
+        # or whether we use the initial alpha used in training the diffusion model.
+        self.initial_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
 
         # standard deviation of the initial noise distribution
         self.init_noise_sigma = 1.0
@@ -215,12 +268,29 @@ class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
             )
 
         self.num_inference_steps = num_inference_steps
-        step_ratio = self.config.num_train_timesteps // self.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 = (np.arange(0, num_inference_steps) * step_ratio).round().copy().astype(np.int64)
+
+        # "leading" and "trailing" corresponds to annotation of Table 1. of https://arxiv.org/abs/2305.08891
+        if self.config.timestep_spacing == "leading":
+            step_ratio = self.config.num_train_timesteps // self.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 = (np.arange(0, num_inference_steps) * step_ratio).round().copy().astype(np.int64)
+            timesteps += self.config.steps_offset
+        elif self.config.timestep_spacing == "trailing":
+            step_ratio = self.config.num_train_timesteps / self.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 = np.round(np.arange(self.config.num_train_timesteps, 0, -step_ratio)[::-1]).astype(np.int64)
+            timesteps -= 1
+        else:
+            raise ValueError(
+                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'leading' or 'trailing'."
+            )
+
+        # Roll timesteps array by one to reflect reversed origin and destination semantics for each step
+        timesteps = np.roll(timesteps, 1)
+        timesteps[0] = int(timesteps[1] - step_ratio)
         self.timesteps = torch.from_numpy(timesteps).to(device)
-        self.timesteps += self.config.steps_offset
 
     def step(
         self,
@@ -237,12 +307,8 @@ class DDIMInverseScheduler(SchedulerMixin, ConfigMixin):
 
         # 2. compute alphas, betas
         # change original implementation to exactly match noise levels for analogous forward process
-        alpha_prod_t = self.alphas_cumprod[timestep]
-        alpha_prod_t_prev = (
-            self.alphas_cumprod[prev_timestep]
-            if prev_timestep < self.config.num_train_timesteps
-            else self.final_alpha_cumprod
-        )
+        alpha_prod_t = self.alphas_cumprod[timestep] if timestep >= 0 else self.initial_alpha_cumprod
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep]
 
         beta_prod_t = 1 - alpha_prod_t
 
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
index a6736b3544..f5c98a551d 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
@@ -138,6 +138,13 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
             guided-diffusion (https://github.com/openai/guided-diffusion) predicts both mean and variance of the
             Gaussian distribution in the model's output. DPM-Solver only needs the "mean" output because it is based on
             diffusion ODEs.
+        timestep_spacing (`str`, default `"linspace"`):
+            The way the timesteps should be scaled. Refer to Table 2. of [Common Diffusion Noise Schedules and Sample
+            Steps are Flawed](https://arxiv.org/abs/2305.08891) for more information.
+        steps_offset (`int`, default `0`):
+            an offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
+            stable diffusion.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -162,6 +169,8 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         use_karras_sigmas: Optional[bool] = False,
         lambda_min_clipped: float = -float("inf"),
         variance_type: Optional[str] = None,
+        timestep_spacing: str = "linspace",
+        steps_offset: int = 0,
     ):
         if trained_betas is not None:
             self.betas = torch.tensor(trained_betas, dtype=torch.float32)
@@ -221,19 +230,41 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
         """
         # Clipping the minimum of all lambda(t) for numerical stability.
         # This is critical for cosine (squaredcos_cap_v2) noise schedule.
-        clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.lambda_min_clipped)
+        clipped_idx = torch.searchsorted(torch.flip(self.lambda_t, [0]), self.lambda_min_clipped).item()
         self.noisiest_timestep = self.config.num_train_timesteps - 1 - clipped_idx
-        timesteps = (
-            np.linspace(0, self.noisiest_timestep, num_inference_steps + 1).round()[:-1].copy().astype(np.int64)
-        )
 
-        if self.use_karras_sigmas:
-            sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
+        # "linspace", "leading", "trailing" corresponds to annotation of Table 2. of https://arxiv.org/abs/2305.08891
+        if self.config.timestep_spacing == "linspace":
+            timesteps = (
+                np.linspace(0, self.noisiest_timestep, num_inference_steps + 1).round()[:-1].copy().astype(np.int64)
+            )
+        elif self.config.timestep_spacing == "leading":
+            step_ratio = (self.noisiest_timestep + 1) // (num_inference_steps + 1)
+            # creates integer timesteps by multiplying by ratio
+            # casting to int to avoid issues when num_inference_step is power of 3
+            timesteps = (np.arange(0, num_inference_steps + 1) * step_ratio).round()[:-1].copy().astype(np.int64)
+            timesteps += self.config.steps_offset
+        elif self.config.timestep_spacing == "trailing":
+            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 = np.arange(self.noisiest_timestep + 1, 0, -step_ratio).round()[::-1].copy().astype(np.int64)
+            timesteps -= 1
+        else:
+            raise ValueError(
+                f"{self.config.timestep_spacing} is not supported. Please make sure to choose one of 'linspace', "
+                "'leading' or 'trailing'."
+            )
+
+        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
+        if self.config.use_karras_sigmas:
             log_sigmas = np.log(sigmas)
             sigmas = self._convert_to_karras(in_sigmas=sigmas, num_inference_steps=num_inference_steps)
             timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas]).round()
             timesteps = timesteps.copy().astype(np.int64)
 
+        self.sigmas = torch.from_numpy(sigmas)
+
         # when num_inference_steps == num_train_timesteps, we can end up with
         # duplicates in timesteps.
         _, unique_indices = np.unique(timesteps, return_index=True)
@@ -397,7 +428,6 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
 
             return epsilon
 
-    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.dpm_solver_first_order_update
     def dpm_solver_first_order_update(
         self,
         model_output: torch.FloatTensor,
@@ -429,23 +459,12 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
             x_t = (sigma_t / sigma_s) * sample - (alpha_t * (torch.exp(-h) - 1.0)) * model_output
         elif self.config.algorithm_type == "dpmsolver":
             x_t = (alpha_t / alpha_s) * sample - (sigma_t * (torch.exp(h) - 1.0)) * model_output
-        elif self.config.algorithm_type == "sde-dpmsolver++":
-            assert noise is not None
-            x_t = (
-                (sigma_t / sigma_s * torch.exp(-h)) * sample
-                + (alpha_t * (1 - torch.exp(-2.0 * h))) * model_output
-                + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
-            )
-        elif self.config.algorithm_type == "sde-dpmsolver":
-            assert noise is not None
-            x_t = (
-                (alpha_t / alpha_s) * sample
-                - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * model_output
-                + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
+        elif "sde" in self.config.algorithm_type:
+            raise NotImplementedError(
+                f"Inversion step is not yet implemented for algorithm type {self.config.algorithm_type}."
             )
         return x_t
 
-    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_second_order_update
     def multistep_dpm_solver_second_order_update(
         self,
         model_output_list: List[torch.FloatTensor],
@@ -504,38 +523,10 @@ class DPMSolverMultistepInverseScheduler(SchedulerMixin, ConfigMixin):
                     - (sigma_t * (torch.exp(h) - 1.0)) * D0
                     - (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
                 )
-        elif self.config.algorithm_type == "sde-dpmsolver++":
-            assert noise is not None
-            if self.config.solver_type == "midpoint":
-                x_t = (
-                    (sigma_t / sigma_s0 * torch.exp(-h)) * sample
-                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
-                    + 0.5 * (alpha_t * (1 - torch.exp(-2.0 * h))) * D1
-                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
-                )
-            elif self.config.solver_type == "heun":
-                x_t = (
-                    (sigma_t / sigma_s0 * torch.exp(-h)) * sample
-                    + (alpha_t * (1 - torch.exp(-2.0 * h))) * D0
-                    + (alpha_t * ((1.0 - torch.exp(-2.0 * h)) / (-2.0 * h) + 1.0)) * D1
-                    + sigma_t * torch.sqrt(1.0 - torch.exp(-2 * h)) * noise
-                )
-        elif self.config.algorithm_type == "sde-dpmsolver":
-            assert noise is not None
-            if self.config.solver_type == "midpoint":
-                x_t = (
-                    (alpha_t / alpha_s0) * sample
-                    - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * D0
-                    - (sigma_t * (torch.exp(h) - 1.0)) * D1
-                    + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
-                )
-            elif self.config.solver_type == "heun":
-                x_t = (
-                    (alpha_t / alpha_s0) * sample
-                    - 2.0 * (sigma_t * (torch.exp(h) - 1.0)) * D0
-                    - 2.0 * (sigma_t * ((torch.exp(h) - 1.0) / h - 1.0)) * D1
-                    + sigma_t * torch.sqrt(torch.exp(2 * h) - 1.0) * noise
-                )
+        elif "sde" in self.config.algorithm_type:
+            raise NotImplementedError(
+                f"Inversion step is not yet implemented for algorithm type {self.config.algorithm_type}."
+            )
         return x_t
 
     # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.multistep_dpm_solver_third_order_update
diff --git a/tests/pipelines/stable_diffusion/test_stable_diffusion_pix2pix_zero.py b/tests/pipelines/stable_diffusion/test_stable_diffusion_pix2pix_zero.py
index 1b17f8b31b..7d94b9f230 100644
--- a/tests/pipelines/stable_diffusion/test_stable_diffusion_pix2pix_zero.py
+++ b/tests/pipelines/stable_diffusion/test_stable_diffusion_pix2pix_zero.py
@@ -220,7 +220,7 @@ class StableDiffusionPix2PixZeroPipelineFastTests(PipelineLatentTesterMixin, Pip
         image = sd_pipe.invert(**inputs).images
         image_slice = image[0, -3:, -3:, -1]
         assert image.shape == (1, 32, 32, 3)
-        expected_slice = np.array([0.4833, 0.4696, 0.5574, 0.5194, 0.5248, 0.5638, 0.5040, 0.5423, 0.5072])
+        expected_slice = np.array([0.4823, 0.4783, 0.5638, 0.5201, 0.5247, 0.5644, 0.5029, 0.5404, 0.5062])
 
         assert np.abs(image_slice.flatten() - expected_slice).max() < 1e-3
 
@@ -235,7 +235,7 @@ class StableDiffusionPix2PixZeroPipelineFastTests(PipelineLatentTesterMixin, Pip
         image = sd_pipe.invert(**inputs).images
         image_slice = image[1, -3:, -3:, -1]
         assert image.shape == (2, 32, 32, 3)
-        expected_slice = np.array([0.6672, 0.5203, 0.4908, 0.4376, 0.4517, 0.5544, 0.4605, 0.4826, 0.5007])
+        expected_slice = np.array([0.6446, 0.5232, 0.4914, 0.4441, 0.4654, 0.5546, 0.4650, 0.4938, 0.5044])
 
         assert np.abs(image_slice.flatten() - expected_slice).max() < 1e-3
 
diff --git a/tests/pipelines/stable_diffusion_2/test_stable_diffusion_diffedit.py b/tests/pipelines/stable_diffusion_2/test_stable_diffusion_diffedit.py
index 1de80d60d8..88aeb50dc1 100644
--- a/tests/pipelines/stable_diffusion_2/test_stable_diffusion_diffedit.py
+++ b/tests/pipelines/stable_diffusion_2/test_stable_diffusion_diffedit.py
@@ -250,7 +250,7 @@ class StableDiffusionDiffEditPipelineFastTests(PipelineLatentTesterMixin, Pipeli
 
         self.assertEqual(image.shape, (2, 32, 32, 3))
         expected_slice = np.array(
-            [0.5150, 0.5134, 0.5043, 0.5376, 0.4694, 0.51050, 0.5015, 0.4407, 0.4799],
+            [0.5150, 0.5134, 0.5043, 0.5376, 0.4694, 0.5105, 0.5015, 0.4407, 0.4799],
         )
         max_diff = np.abs(image_slice.flatten() - expected_slice).max()
         self.assertLessEqual(max_diff, 1e-3)
@@ -277,7 +277,7 @@ class StableDiffusionDiffEditPipelineFastTests(PipelineLatentTesterMixin, Pipeli
 
         self.assertEqual(image.shape, (2, 32, 32, 3))
         expected_slice = np.array(
-            [0.5150, 0.5134, 0.5043, 0.5376, 0.4694, 0.51050, 0.5015, 0.4407, 0.4799],
+            [0.5305, 0.4673, 0.5314, 0.5308, 0.4886, 0.5279, 0.5142, 0.4724, 0.4892],
         )
         max_diff = np.abs(image_slice.flatten() - expected_slice).max()
         self.assertLessEqual(max_diff, 1e-3)
diff --git a/tests/schedulers/test_scheduler_ddim_inverse.py b/tests/schedulers/test_scheduler_ddim_inverse.py
new file mode 100644
index 0000000000..39ee26306c
--- /dev/null
+++ b/tests/schedulers/test_scheduler_ddim_inverse.py
@@ -0,0 +1,135 @@
+import torch
+
+from diffusers import DDIMInverseScheduler
+
+from .test_schedulers import SchedulerCommonTest
+
+
+class DDIMInverseSchedulerTest(SchedulerCommonTest):
+    scheduler_classes = (DDIMInverseScheduler,)
+    forward_default_kwargs = (("eta", 0.0), ("num_inference_steps", 50))
+
+    def get_scheduler_config(self, **kwargs):
+        config = {
+            "num_train_timesteps": 1000,
+            "beta_start": 0.0001,
+            "beta_end": 0.02,
+            "beta_schedule": "linear",
+            "clip_sample": True,
+        }
+
+        config.update(**kwargs)
+        return config
+
+    def full_loop(self, **config):
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(**config)
+        scheduler = scheduler_class(**scheduler_config)
+
+        num_inference_steps, eta = 10, 0.0
+
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter
+
+        scheduler.set_timesteps(num_inference_steps)
+
+        for t in scheduler.timesteps:
+            residual = model(sample, t)
+            sample = scheduler.step(residual, t, sample, eta).prev_sample
+
+        return sample
+
+    def test_timesteps(self):
+        for timesteps in [100, 500, 1000]:
+            self.check_over_configs(num_train_timesteps=timesteps)
+
+    def test_steps_offset(self):
+        for steps_offset in [0, 1]:
+            self.check_over_configs(steps_offset=steps_offset)
+
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(steps_offset=1)
+        scheduler = scheduler_class(**scheduler_config)
+        scheduler.set_timesteps(5)
+        assert torch.equal(scheduler.timesteps, torch.LongTensor([-199, 1, 201, 401, 601]))
+
+    def test_betas(self):
+        for beta_start, beta_end in zip([0.0001, 0.001, 0.01, 0.1], [0.002, 0.02, 0.2, 2]):
+            self.check_over_configs(beta_start=beta_start, beta_end=beta_end)
+
+    def test_schedules(self):
+        for schedule in ["linear", "squaredcos_cap_v2"]:
+            self.check_over_configs(beta_schedule=schedule)
+
+    def test_prediction_type(self):
+        for prediction_type in ["epsilon", "v_prediction"]:
+            self.check_over_configs(prediction_type=prediction_type)
+
+    def test_clip_sample(self):
+        for clip_sample in [True, False]:
+            self.check_over_configs(clip_sample=clip_sample)
+
+    def test_timestep_spacing(self):
+        for timestep_spacing in ["trailing", "leading"]:
+            self.check_over_configs(timestep_spacing=timestep_spacing)
+
+    def test_rescale_betas_zero_snr(self):
+        for rescale_betas_zero_snr in [True, False]:
+            self.check_over_configs(rescale_betas_zero_snr=rescale_betas_zero_snr)
+
+    def test_thresholding(self):
+        self.check_over_configs(thresholding=False)
+        for threshold in [0.5, 1.0, 2.0]:
+            for prediction_type in ["epsilon", "v_prediction"]:
+                self.check_over_configs(
+                    thresholding=True,
+                    prediction_type=prediction_type,
+                    sample_max_value=threshold,
+                )
+
+    def test_time_indices(self):
+        for t in [1, 10, 49]:
+            self.check_over_forward(time_step=t)
+
+    def test_inference_steps(self):
+        for t, num_inference_steps in zip([1, 10, 50], [10, 50, 500]):
+            self.check_over_forward(time_step=t, num_inference_steps=num_inference_steps)
+
+    def test_add_noise_device(self):
+        pass
+
+    def test_full_loop_no_noise(self):
+        sample = self.full_loop()
+
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_sum.item() - 509.1079) < 1e-2
+        assert abs(result_mean.item() - 0.6629) < 1e-3
+
+    def test_full_loop_with_v_prediction(self):
+        sample = self.full_loop(prediction_type="v_prediction")
+
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_sum.item() - 1029.129) < 1e-2
+        assert abs(result_mean.item() - 1.3400) < 1e-3
+
+    def test_full_loop_with_set_alpha_to_one(self):
+        # We specify different beta, so that the first alpha is 0.99
+        sample = self.full_loop(set_alpha_to_one=True, beta_start=0.01)
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_sum.item() - 259.8116) < 1e-2
+        assert abs(result_mean.item() - 0.3383) < 1e-3
+
+    def test_full_loop_with_no_set_alpha_to_one(self):
+        # We specify different beta, so that the first alpha is 0.99
+        sample = self.full_loop(set_alpha_to_one=False, beta_start=0.01)
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_sum.item() - 239.055) < 1e-2
+        assert abs(result_mean.item() - 0.3113) < 1e-3
diff --git a/tests/schedulers/test_scheduler_dpm_multi_inverse.py b/tests/schedulers/test_scheduler_dpm_multi_inverse.py
new file mode 100644
index 0000000000..61a1d82e0f
--- /dev/null
+++ b/tests/schedulers/test_scheduler_dpm_multi_inverse.py
@@ -0,0 +1,266 @@
+import tempfile
+
+import torch
+
+from diffusers import DPMSolverMultistepInverseScheduler, DPMSolverMultistepScheduler
+
+from .test_schedulers import SchedulerCommonTest
+
+
+class DPMSolverMultistepSchedulerTest(SchedulerCommonTest):
+    scheduler_classes = (DPMSolverMultistepInverseScheduler,)
+    forward_default_kwargs = (("num_inference_steps", 25),)
+
+    def get_scheduler_config(self, **kwargs):
+        config = {
+            "num_train_timesteps": 1000,
+            "beta_start": 0.0001,
+            "beta_end": 0.02,
+            "beta_schedule": "linear",
+            "solver_order": 2,
+            "prediction_type": "epsilon",
+            "thresholding": False,
+            "sample_max_value": 1.0,
+            "algorithm_type": "dpmsolver++",
+            "solver_type": "midpoint",
+            "lower_order_final": False,
+            "lambda_min_clipped": -float("inf"),
+            "variance_type": None,
+        }
+
+        config.update(**kwargs)
+        return config
+
+    def check_over_configs(self, time_step=0, **config):
+        kwargs = dict(self.forward_default_kwargs)
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+        sample = self.dummy_sample
+        residual = 0.1 * sample
+        dummy_past_residuals = [residual + 0.2, residual + 0.15, residual + 0.10]
+
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config(**config)
+            scheduler = scheduler_class(**scheduler_config)
+            scheduler.set_timesteps(num_inference_steps)
+            # copy over dummy past residuals
+            scheduler.model_outputs = dummy_past_residuals[: scheduler.config.solver_order]
+
+            with tempfile.TemporaryDirectory() as tmpdirname:
+                scheduler.save_config(tmpdirname)
+                new_scheduler = scheduler_class.from_pretrained(tmpdirname)
+                new_scheduler.set_timesteps(num_inference_steps)
+                # copy over dummy past residuals
+                new_scheduler.model_outputs = dummy_past_residuals[: new_scheduler.config.solver_order]
+
+            output, new_output = sample, sample
+            for t in range(time_step, time_step + scheduler.config.solver_order + 1):
+                output = scheduler.step(residual, t, output, **kwargs).prev_sample
+                new_output = new_scheduler.step(residual, t, new_output, **kwargs).prev_sample
+
+                assert torch.sum(torch.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
+
+    def test_from_save_pretrained(self):
+        pass
+
+    def check_over_forward(self, time_step=0, **forward_kwargs):
+        kwargs = dict(self.forward_default_kwargs)
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+        sample = self.dummy_sample
+        residual = 0.1 * sample
+        dummy_past_residuals = [residual + 0.2, residual + 0.15, residual + 0.10]
+
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config()
+            scheduler = scheduler_class(**scheduler_config)
+            scheduler.set_timesteps(num_inference_steps)
+
+            # copy over dummy past residuals (must be after setting timesteps)
+            scheduler.model_outputs = dummy_past_residuals[: scheduler.config.solver_order]
+
+            with tempfile.TemporaryDirectory() as tmpdirname:
+                scheduler.save_config(tmpdirname)
+                new_scheduler = scheduler_class.from_pretrained(tmpdirname)
+                # copy over dummy past residuals
+                new_scheduler.set_timesteps(num_inference_steps)
+
+                # copy over dummy past residual (must be after setting timesteps)
+                new_scheduler.model_outputs = dummy_past_residuals[: new_scheduler.config.solver_order]
+
+            output = scheduler.step(residual, time_step, sample, **kwargs).prev_sample
+            new_output = new_scheduler.step(residual, time_step, sample, **kwargs).prev_sample
+
+            assert torch.sum(torch.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
+
+    def full_loop(self, scheduler=None, **config):
+        if scheduler is None:
+            scheduler_class = self.scheduler_classes[0]
+            scheduler_config = self.get_scheduler_config(**config)
+            scheduler = scheduler_class(**scheduler_config)
+
+        num_inference_steps = 10
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter
+        scheduler.set_timesteps(num_inference_steps)
+
+        for i, t in enumerate(scheduler.timesteps):
+            residual = model(sample, t)
+            sample = scheduler.step(residual, t, sample).prev_sample
+
+        return sample
+
+    def test_step_shape(self):
+        kwargs = dict(self.forward_default_kwargs)
+
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config()
+            scheduler = scheduler_class(**scheduler_config)
+
+            sample = self.dummy_sample
+            residual = 0.1 * sample
+
+            if num_inference_steps is not None and hasattr(scheduler, "set_timesteps"):
+                scheduler.set_timesteps(num_inference_steps)
+            elif num_inference_steps is not None and not hasattr(scheduler, "set_timesteps"):
+                kwargs["num_inference_steps"] = num_inference_steps
+
+            # copy over dummy past residuals (must be done after set_timesteps)
+            dummy_past_residuals = [residual + 0.2, residual + 0.15, residual + 0.10]
+            scheduler.model_outputs = dummy_past_residuals[: scheduler.config.solver_order]
+
+            time_step_0 = scheduler.timesteps[5]
+            time_step_1 = scheduler.timesteps[6]
+
+            output_0 = scheduler.step(residual, time_step_0, sample, **kwargs).prev_sample
+            output_1 = scheduler.step(residual, time_step_1, sample, **kwargs).prev_sample
+
+            self.assertEqual(output_0.shape, sample.shape)
+            self.assertEqual(output_0.shape, output_1.shape)
+
+    def test_timesteps(self):
+        for timesteps in [25, 50, 100, 999, 1000]:
+            self.check_over_configs(num_train_timesteps=timesteps)
+
+    def test_thresholding(self):
+        self.check_over_configs(thresholding=False)
+        for order in [1, 2, 3]:
+            for solver_type in ["midpoint", "heun"]:
+                for threshold in [0.5, 1.0, 2.0]:
+                    for prediction_type in ["epsilon", "sample"]:
+                        self.check_over_configs(
+                            thresholding=True,
+                            prediction_type=prediction_type,
+                            sample_max_value=threshold,
+                            algorithm_type="dpmsolver++",
+                            solver_order=order,
+                            solver_type=solver_type,
+                        )
+
+    def test_prediction_type(self):
+        for prediction_type in ["epsilon", "v_prediction"]:
+            self.check_over_configs(prediction_type=prediction_type)
+
+    def test_solver_order_and_type(self):
+        for algorithm_type in ["dpmsolver", "dpmsolver++"]:
+            for solver_type in ["midpoint", "heun"]:
+                for order in [1, 2, 3]:
+                    for prediction_type in ["epsilon", "sample"]:
+                        self.check_over_configs(
+                            solver_order=order,
+                            solver_type=solver_type,
+                            prediction_type=prediction_type,
+                            algorithm_type=algorithm_type,
+                        )
+                        sample = self.full_loop(
+                            solver_order=order,
+                            solver_type=solver_type,
+                            prediction_type=prediction_type,
+                            algorithm_type=algorithm_type,
+                        )
+                        assert not torch.isnan(sample).any(), "Samples have nan numbers"
+
+    def test_lower_order_final(self):
+        self.check_over_configs(lower_order_final=True)
+        self.check_over_configs(lower_order_final=False)
+
+    def test_lambda_min_clipped(self):
+        self.check_over_configs(lambda_min_clipped=-float("inf"))
+        self.check_over_configs(lambda_min_clipped=-5.1)
+
+    def test_variance_type(self):
+        self.check_over_configs(variance_type=None)
+        self.check_over_configs(variance_type="learned_range")
+
+    def test_timestep_spacing(self):
+        for timestep_spacing in ["trailing", "leading"]:
+            self.check_over_configs(timestep_spacing=timestep_spacing)
+
+    def test_inference_steps(self):
+        for num_inference_steps in [1, 2, 3, 5, 10, 50, 100, 999, 1000]:
+            self.check_over_forward(num_inference_steps=num_inference_steps, time_step=0)
+
+    def test_full_loop_no_noise(self):
+        sample = self.full_loop()
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 0.7047) < 1e-3
+
+    def test_full_loop_no_noise_thres(self):
+        sample = self.full_loop(thresholding=True, dynamic_thresholding_ratio=0.87, sample_max_value=0.5)
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 19.8933) < 1e-3
+
+    def test_full_loop_with_v_prediction(self):
+        sample = self.full_loop(prediction_type="v_prediction")
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 1.5194) < 1e-3
+
+    def test_full_loop_with_karras_and_v_prediction(self):
+        sample = self.full_loop(prediction_type="v_prediction", use_karras_sigmas=True)
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 1.7833) < 1e-3
+
+    def test_switch(self):
+        # make sure that iterating over schedulers with same config names gives same results
+        # for defaults
+        scheduler = DPMSolverMultistepInverseScheduler(**self.get_scheduler_config())
+        sample = self.full_loop(scheduler=scheduler)
+        result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(result_mean.item() - 0.7047) < 1e-3
+
+        scheduler = DPMSolverMultistepScheduler.from_config(scheduler.config)
+        scheduler = DPMSolverMultistepInverseScheduler.from_config(scheduler.config)
+
+        sample = self.full_loop(scheduler=scheduler)
+        new_result_mean = torch.mean(torch.abs(sample))
+
+        assert abs(new_result_mean.item() - result_mean.item()) < 1e-3
+
+    def test_fp16_support(self):
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(thresholding=True, dynamic_thresholding_ratio=0)
+        scheduler = scheduler_class(**scheduler_config)
+
+        num_inference_steps = 10
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter.half()
+        scheduler.set_timesteps(num_inference_steps)
+
+        for i, t in enumerate(scheduler.timesteps):
+            residual = model(sample, t)
+            sample = scheduler.step(residual, t, sample).prev_sample
+
+        assert sample.dtype == torch.float16
+
+    def test_unique_timesteps(self, **config):
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config(**config)
+            scheduler = scheduler_class(**scheduler_config)
+
+            scheduler.set_timesteps(scheduler.config.num_train_timesteps)
+            assert len(scheduler.timesteps.unique()) == scheduler.num_inference_steps