diff --git a/src/diffusers/models/unet_glide.py b/src/diffusers/models/unet_glide.py
index 39376f3699..e26fcbdd4c 100644
--- a/src/diffusers/models/unet_glide.py
+++ b/src/diffusers/models/unet_glide.py
@@ -438,8 +438,8 @@ class GlideTextToImageUNetModel(GlideUNetModel):
 
         self.transformer_proj = nn.Linear(transformer_dim, self.model_channels * 4)
 
-    def forward(self, sample, step_value, transformer_out=None):
-        timesteps = step_value
+    def forward(self, sample, timestep, transformer_out=None):
+        timesteps = timestep
         x = sample
         hs = []
         emb = self.time_embed(
@@ -530,8 +530,8 @@ class GlideSuperResUNetModel(GlideUNetModel):
             resblock_updown=resblock_updown,
         )
 
-    def forward(self, sample, step_value, low_res=None):
-        timesteps = step_value
+    def forward(self, sample, timestep, low_res=None):
+        timesteps = timestep
         x = sample
         _, _, new_height, new_width = x.shape
         upsampled = F.interpolate(low_res, (new_height, new_width), mode="bilinear")
diff --git a/src/diffusers/models/unet_sde_score_estimation.py b/src/diffusers/models/unet_sde_score_estimation.py
index 339a9f6550..198af814a7 100644
--- a/src/diffusers/models/unet_sde_score_estimation.py
+++ b/src/diffusers/models/unet_sde_score_estimation.py
@@ -323,8 +323,8 @@ class NCSNpp(ModelMixin, ConfigMixin):
 
         self.all_modules = nn.ModuleList(modules)
 
-    def forward(self, sample, step_value, sigmas=None):
-        timesteps = step_value
+    def forward(self, sample, timestep, sigmas=None):
+        timesteps = timestep
         x = sample
         # timestep/noise_level embedding; only for continuous training
         modules = self.all_modules
diff --git a/src/diffusers/models/unet_unconditional.py b/src/diffusers/models/unet_unconditional.py
index 5495ccd6ea..ad738a2737 100644
--- a/src/diffusers/models/unet_unconditional.py
+++ b/src/diffusers/models/unet_unconditional.py
@@ -254,7 +254,7 @@ class UNetUnconditionalModel(ModelMixin, ConfigMixin):
         # ======================================
 
     def forward(
-        self, sample: torch.FloatTensor, step_value: Union[torch.Tensor, float, int]
+        self, sample: torch.FloatTensor, timestep: Union[torch.Tensor, float, int]
     ) -> Dict[str, torch.FloatTensor]:
         # TODO(PVP) - to delete later at release
         # IMPORTANT: NOT RELEVANT WHEN REVIEWING API
@@ -263,10 +263,12 @@ class UNetUnconditionalModel(ModelMixin, ConfigMixin):
             self.set_weights()
         # ======================================
 
-        # 1. time step embeddings
-        timesteps = step_value
+        # 1. time step embeddings -> make correct tensor
+        timesteps = timestep
         if not torch.is_tensor(timesteps):
             timesteps = torch.tensor([timesteps], dtype=torch.long, device=sample.device)
+        elif torch.is_tensor(timesteps) and len(timesteps.shape) == 0:
+            timesteps = timesteps[None].to(sample.device)
 
         t_emb = get_timestep_embedding(
             timesteps,
diff --git a/src/diffusers/pipelines/ddim/pipeline_ddim.py b/src/diffusers/pipelines/ddim/pipeline_ddim.py
index 2d7e72c77b..d0e920febb 100644
--- a/src/diffusers/pipelines/ddim/pipeline_ddim.py
+++ b/src/diffusers/pipelines/ddim/pipeline_ddim.py
@@ -22,19 +22,16 @@ from ...pipeline_utils import DiffusionPipeline
 
 
 class DDIMPipeline(DiffusionPipeline):
-    def __init__(self, unet, noise_scheduler):
+    def __init__(self, unet, scheduler):
         super().__init__()
-        noise_scheduler = noise_scheduler.set_format("pt")
-        self.register_modules(unet=unet, noise_scheduler=noise_scheduler)
+        scheduler = scheduler.set_format("pt")
+        self.register_modules(unet=unet, scheduler=scheduler)
 
     def __call__(self, batch_size=1, generator=None, torch_device=None, eta=0.0, num_inference_steps=50):
         # eta corresponds to η in paper and should be between [0, 1]
         if torch_device is None:
             torch_device = "cuda" if torch.cuda.is_available() else "cpu"
 
-        num_trained_timesteps = self.noise_scheduler.config.timesteps
-        inference_step_times = range(0, num_trained_timesteps, num_trained_timesteps // num_inference_steps)
-
         self.unet.to(torch_device)
 
         # Sample gaussian noise to begin loop
@@ -44,34 +41,19 @@ class DDIMPipeline(DiffusionPipeline):
         )
         image = image.to(torch_device)
 
-        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
-        # Ideally, read DDIM paper in-detail understanding
+        # set step values
+        self.scheduler.set_timesteps(num_inference_steps)
 
-        # Notation (<variable name> -> <name in paper>
-        # - pred_noise_t -> e_theta(x_t, t)
-        # - pred_original_image -> f_theta(x_t, t) or x_0
-        # - std_dev_t -> sigma_t
-        # - eta -> η
-        # - pred_image_direction -> "direction pointingc to x_t"
-        # - pred_prev_image -> "x_t-1"
-        for t in tqdm.tqdm(reversed(range(num_inference_steps)), total=num_inference_steps):
+        for t in tqdm.tqdm(self.scheduler.timesteps):
             # 1. predict noise residual
             with torch.no_grad():
-                residual = self.unet(image, inference_step_times[t])
+                residual = self.unet(image, t)
 
                 if isinstance(residual, dict):
                     residual = residual["sample"]
 
-            # 2. predict previous mean of image x_t-1
-            pred_prev_image = self.noise_scheduler.step(residual, image, t, num_inference_steps, eta)
+            # 2. predict previous mean of image x_t-1 and add variance depending on eta
+            # do x_t -> x_t-1
+            image = self.scheduler.step(residual, t, image, eta)["prev_sample"]
 
-            # 3. optionally sample variance
-            variance = 0
-            if eta > 0:
-                noise = torch.randn(image.shape, generator=generator).to(image.device)
-                variance = self.noise_scheduler.get_variance(t, num_inference_steps).sqrt() * eta * noise
-
-            # 4. set current image to prev_image: x_t -> x_t-1
-            image = pred_prev_image + variance
-
-        return image
+        return {"sample": image}
diff --git a/src/diffusers/pipelines/ddpm/pipeline_ddpm.py b/src/diffusers/pipelines/ddpm/pipeline_ddpm.py
index 2d18e43c9c..d0949b27bb 100644
--- a/src/diffusers/pipelines/ddpm/pipeline_ddpm.py
+++ b/src/diffusers/pipelines/ddpm/pipeline_ddpm.py
@@ -22,10 +22,10 @@ from ...pipeline_utils import DiffusionPipeline
 
 
 class DDPMPipeline(DiffusionPipeline):
-    def __init__(self, unet, noise_scheduler):
+    def __init__(self, unet, scheduler):
         super().__init__()
-        noise_scheduler = noise_scheduler.set_format("pt")
-        self.register_modules(unet=unet, noise_scheduler=noise_scheduler)
+        scheduler = scheduler.set_format("pt")
+        self.register_modules(unet=unet, scheduler=scheduler)
 
     def __call__(self, batch_size=1, generator=None, torch_device=None):
         if torch_device is None:
@@ -40,7 +40,7 @@ class DDPMPipeline(DiffusionPipeline):
         )
         image = image.to(torch_device)
 
-        num_prediction_steps = len(self.noise_scheduler)
+        num_prediction_steps = len(self.scheduler)
         for t in tqdm.tqdm(reversed(range(num_prediction_steps)), total=num_prediction_steps):
             # 1. predict noise residual
             with torch.no_grad():
@@ -50,13 +50,13 @@ class DDPMPipeline(DiffusionPipeline):
                     residual = residual["sample"]
 
             # 2. predict previous mean of image x_t-1
-            pred_prev_image = self.noise_scheduler.step(residual, image, t)
+            pred_prev_image = self.scheduler.step(residual, t, image)["prev_sample"]
 
             # 3. optionally sample variance
             variance = 0
             if t > 0:
                 noise = torch.randn(image.shape, generator=generator).to(image.device)
-                variance = self.noise_scheduler.get_variance(t).sqrt() * noise
+                variance = self.scheduler.get_variance(t).sqrt() * noise
 
             # 4. set current image to prev_image: x_t -> x_t-1
             image = pred_prev_image + variance
diff --git a/src/diffusers/pipelines/glide/pipeline_glide.py b/src/diffusers/pipelines/glide/pipeline_glide.py
index a9b6746f5c..c0ccb80477 100644
--- a/src/diffusers/pipelines/glide/pipeline_glide.py
+++ b/src/diffusers/pipelines/glide/pipeline_glide.py
@@ -713,20 +713,20 @@ class GlidePipeline(DiffusionPipeline):
     def __init__(
         self,
         text_unet: GlideTextToImageUNetModel,
-        text_noise_scheduler: DDPMScheduler,
+        text_scheduler: DDPMScheduler,
         text_encoder: CLIPTextModel,
         tokenizer: GPT2Tokenizer,
         upscale_unet: GlideSuperResUNetModel,
-        upscale_noise_scheduler: DDIMScheduler,
+        upscale_scheduler: DDIMScheduler,
     ):
         super().__init__()
         self.register_modules(
             text_unet=text_unet,
-            text_noise_scheduler=text_noise_scheduler,
+            text_scheduler=text_scheduler,
             text_encoder=text_encoder,
             tokenizer=tokenizer,
             upscale_unet=upscale_unet,
-            upscale_noise_scheduler=upscale_noise_scheduler,
+            upscale_scheduler=upscale_scheduler,
         )
 
     @torch.no_grad()
@@ -777,20 +777,20 @@ class GlidePipeline(DiffusionPipeline):
         transformer_out = self.text_encoder(input_ids, attention_mask).last_hidden_state
 
         # 3. Run the text2image generation step
-        num_prediction_steps = len(self.text_noise_scheduler)
+        num_prediction_steps = len(self.text_scheduler)
         for t in tqdm.tqdm(reversed(range(num_prediction_steps)), total=num_prediction_steps):
             with torch.no_grad():
                 time_input = torch.tensor([t] * image.shape[0], device=torch_device)
                 model_output = text_model_fn(image, time_input, transformer_out)
                 noise_residual, model_var_values = torch.split(model_output, 3, dim=1)
 
-            min_log = self.text_noise_scheduler.get_variance(t, "fixed_small_log")
-            max_log = self.text_noise_scheduler.get_variance(t, "fixed_large_log")
+            min_log = self.text_scheduler.get_variance(t, "fixed_small_log")
+            max_log = self.text_scheduler.get_variance(t, "fixed_large_log")
             # The model_var_values is [-1, 1] for [min_var, max_var].
             frac = (model_var_values + 1) / 2
             model_log_variance = frac * max_log + (1 - frac) * min_log
 
-            pred_prev_image = self.text_noise_scheduler.step(noise_residual, image, t)
+            pred_prev_image = self.text_scheduler.step(noise_residual, image, t)
             noise = torch.randn(image.shape, generator=generator).to(torch_device)
             variance = torch.exp(0.5 * model_log_variance) * noise
 
@@ -814,7 +814,7 @@ class GlidePipeline(DiffusionPipeline):
         ).to(torch_device)
         image = image * upsample_temp
 
-        num_trained_timesteps = self.upscale_noise_scheduler.timesteps
+        num_trained_timesteps = self.upscale_scheduler.timesteps
         inference_step_times = range(0, num_trained_timesteps, num_trained_timesteps // num_inference_steps_upscale)
 
         for t in tqdm.tqdm(reversed(range(num_inference_steps_upscale)), total=num_inference_steps_upscale):
@@ -825,7 +825,7 @@ class GlidePipeline(DiffusionPipeline):
                 noise_residual, pred_variance = torch.split(model_output, 3, dim=1)
 
             # 2. predict previous mean of image x_t-1
-            pred_prev_image = self.upscale_noise_scheduler.step(
+            pred_prev_image = self.upscale_scheduler.step(
                 noise_residual, image, t, num_inference_steps_upscale, eta, use_clipped_residual=True
             )
 
@@ -833,9 +833,7 @@ class GlidePipeline(DiffusionPipeline):
             variance = 0
             if eta > 0:
                 noise = torch.randn(image.shape, generator=generator).to(torch_device)
-                variance = (
-                    self.upscale_noise_scheduler.get_variance(t, num_inference_steps_upscale).sqrt() * eta * noise
-                )
+                variance = self.upscale_scheduler.get_variance(t, num_inference_steps_upscale).sqrt() * eta * noise
 
             # 4. set current image to prev_image: x_t -> x_t-1
             image = pred_prev_image + variance
diff --git a/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py b/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py
index 6a4eb1621f..6711d2aba3 100644
--- a/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py
+++ b/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py
@@ -545,10 +545,10 @@ class LDMBertModel(LDMBertPreTrainedModel):
 
 
 class LatentDiffusionPipeline(DiffusionPipeline):
-    def __init__(self, vqvae, bert, tokenizer, unet, noise_scheduler):
+    def __init__(self, vqvae, bert, tokenizer, unet, scheduler):
         super().__init__()
-        noise_scheduler = noise_scheduler.set_format("pt")
-        self.register_modules(vqvae=vqvae, bert=bert, tokenizer=tokenizer, unet=unet, noise_scheduler=noise_scheduler)
+        scheduler = scheduler.set_format("pt")
+        self.register_modules(vqvae=vqvae, bert=bert, tokenizer=tokenizer, unet=unet, scheduler=scheduler)
 
     @torch.no_grad()
     def __call__(
@@ -581,7 +581,7 @@ class LatentDiffusionPipeline(DiffusionPipeline):
         text_input = self.tokenizer(prompt, padding="max_length", max_length=77, return_tensors="pt").to(torch_device)
         text_embedding = self.bert(text_input.input_ids)
 
-        num_trained_timesteps = self.noise_scheduler.config.timesteps
+        num_trained_timesteps = self.scheduler.config.timesteps
         inference_step_times = range(0, num_trained_timesteps, num_trained_timesteps // num_inference_steps)
 
         image = torch.randn(
@@ -622,13 +622,13 @@ class LatentDiffusionPipeline(DiffusionPipeline):
                 pred_noise_t = pred_noise_t_uncond + guidance_scale * (pred_noise_t - pred_noise_t_uncond)
 
             # 2. predict previous mean of image x_t-1
-            pred_prev_image = self.noise_scheduler.step(pred_noise_t, image, t, num_inference_steps, eta)
+            pred_prev_image = self.scheduler.step(pred_noise_t, image, t, num_inference_steps, eta)
 
             # 3. optionally sample variance
             variance = 0
             if eta > 0:
                 noise = torch.randn(image.shape, generator=generator).to(image.device)
-                variance = self.noise_scheduler.get_variance(t, num_inference_steps).sqrt() * eta * noise
+                variance = self.scheduler.get_variance(t, num_inference_steps).sqrt() * eta * noise
 
             # 4. set current image to prev_image: x_t -> x_t-1
             image = pred_prev_image + variance
diff --git a/src/diffusers/pipelines/latent_diffusion_uncond/pipeline_latent_diffusion_uncond.py b/src/diffusers/pipelines/latent_diffusion_uncond/pipeline_latent_diffusion_uncond.py
index 30aafc1e8e..d1918482e1 100644
--- a/src/diffusers/pipelines/latent_diffusion_uncond/pipeline_latent_diffusion_uncond.py
+++ b/src/diffusers/pipelines/latent_diffusion_uncond/pipeline_latent_diffusion_uncond.py
@@ -6,10 +6,10 @@ from ...pipeline_utils import DiffusionPipeline
 
 
 class LatentDiffusionUncondPipeline(DiffusionPipeline):
-    def __init__(self, vqvae, unet, noise_scheduler):
+    def __init__(self, vqvae, unet, scheduler):
         super().__init__()
-        noise_scheduler = noise_scheduler.set_format("pt")
-        self.register_modules(vqvae=vqvae, unet=unet, noise_scheduler=noise_scheduler)
+        scheduler = scheduler.set_format("pt")
+        self.register_modules(vqvae=vqvae, unet=unet, scheduler=scheduler)
 
     @torch.no_grad()
     def __call__(
@@ -28,44 +28,23 @@ class LatentDiffusionUncondPipeline(DiffusionPipeline):
         self.unet.to(torch_device)
         self.vqvae.to(torch_device)
 
-        num_trained_timesteps = self.noise_scheduler.config.timesteps
-        inference_step_times = range(0, num_trained_timesteps, num_trained_timesteps // num_inference_steps)
-
         image = torch.randn(
             (batch_size, self.unet.in_channels, self.unet.image_size, self.unet.image_size),
             generator=generator,
         ).to(torch_device)
 
-        # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
-        # Ideally, read DDIM paper in-detail understanding
+        self.scheduler.set_timesteps(num_inference_steps)
 
-        # Notation (<variable name> -> <name in paper>
-        # - pred_noise_t -> e_theta(x_t, t)
-        # - pred_original_image -> f_theta(x_t, t) or x_0
-        # - std_dev_t -> sigma_t
-        # - eta -> η
-        # - pred_image_direction -> "direction pointingc to x_t"
-        # - pred_prev_image -> "x_t-1"
-        for t in tqdm.tqdm(reversed(range(num_inference_steps)), total=num_inference_steps):
-            # 1. predict noise residual
-            timesteps = torch.tensor([inference_step_times[t]] * image.shape[0], device=torch_device)
-            pred_noise_t = self.unet(image, timesteps)
+        for t in tqdm.tqdm(self.scheduler.timesteps):
+            residual = self.unet(image, t)
 
-            if isinstance(pred_noise_t, dict):
-                pred_noise_t = pred_noise_t["sample"]
+            if isinstance(residual, dict):
+                residual = residual["sample"]
 
-            # 2. predict previous mean of image x_t-1
-            pred_prev_image = self.noise_scheduler.step(pred_noise_t, image, t, num_inference_steps, eta)
-
-            # 3. optionally sample variance
-            variance = 0
-            if eta > 0:
-                noise = torch.randn(image.shape, generator=generator).to(image.device)
-                variance = self.noise_scheduler.get_variance(t, num_inference_steps).sqrt() * eta * noise
-
-            # 4. set current image to prev_image: x_t -> x_t-1
-            image = pred_prev_image + variance
+            # 2. predict previous mean of image x_t-1 and add variance depending on eta
+            # do x_t -> x_t-1
+            image = self.scheduler.step(residual, t, image, eta)["prev_sample"]
 
         # decode image with vae
         image = self.vqvae.decode(image)
-        return image
+        return {"sample": image}
diff --git a/src/diffusers/pipelines/pndm/pipeline_pndm.py b/src/diffusers/pipelines/pndm/pipeline_pndm.py
index 7dbff9b1b9..9dc7e92ede 100644
--- a/src/diffusers/pipelines/pndm/pipeline_pndm.py
+++ b/src/diffusers/pipelines/pndm/pipeline_pndm.py
@@ -22,10 +22,10 @@ from ...pipeline_utils import DiffusionPipeline
 
 
 class PNDMPipeline(DiffusionPipeline):
-    def __init__(self, unet, noise_scheduler):
+    def __init__(self, unet, scheduler):
         super().__init__()
-        noise_scheduler = noise_scheduler.set_format("pt")
-        self.register_modules(unet=unet, noise_scheduler=noise_scheduler)
+        scheduler = scheduler.set_format("pt")
+        self.register_modules(unet=unet, scheduler=scheduler)
 
     def __call__(self, batch_size=1, generator=None, torch_device=None, num_inference_steps=50):
         # For more information on the sampling method you can take a look at Algorithm 2 of
@@ -42,7 +42,7 @@ class PNDMPipeline(DiffusionPipeline):
         )
         image = image.to(torch_device)
 
-        prk_time_steps = self.noise_scheduler.get_prk_time_steps(num_inference_steps)
+        prk_time_steps = self.scheduler.get_prk_time_steps(num_inference_steps)
         for t in tqdm.tqdm(range(len(prk_time_steps))):
             t_orig = prk_time_steps[t]
             residual = self.unet(image, t_orig)
@@ -50,9 +50,9 @@ class PNDMPipeline(DiffusionPipeline):
             if isinstance(residual, dict):
                 residual = residual["sample"]
 
-            image = self.noise_scheduler.step_prk(residual, image, t, num_inference_steps)
+            image = self.scheduler.step_prk(residual, t, image, num_inference_steps)["prev_sample"]
 
-        timesteps = self.noise_scheduler.get_time_steps(num_inference_steps)
+        timesteps = self.scheduler.get_time_steps(num_inference_steps)
         for t in tqdm.tqdm(range(len(timesteps))):
             t_orig = timesteps[t]
             residual = self.unet(image, t_orig)
@@ -60,6 +60,6 @@ class PNDMPipeline(DiffusionPipeline):
             if isinstance(residual, dict):
                 residual = residual["sample"]
 
-            image = self.noise_scheduler.step_plms(residual, image, t, num_inference_steps)
+            image = self.scheduler.step_plms(residual, t, image, num_inference_steps)["prev_sample"]
 
         return image
diff --git a/src/diffusers/schedulers/scheduling_ddim.py b/src/diffusers/schedulers/scheduling_ddim.py
index 97b5880c0b..89c7a52914 100644
--- a/src/diffusers/schedulers/scheduling_ddim.py
+++ b/src/diffusers/schedulers/scheduling_ddim.py
@@ -16,8 +16,10 @@
 # and https://github.com/hojonathanho/diffusion
 
 import math
+from typing import Union
 
 import numpy as np
+import torch
 
 from ..configuration_utils import ConfigMixin
 from .scheduling_utils import SchedulerMixin
@@ -84,14 +86,16 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         self.alphas_cumprod = np.cumprod(self.alphas, axis=0)
         self.one = np.array(1.0)
 
+        # setable values
+        self.num_inference_steps = None
+        self.timesteps = np.arange(0, self.config.timesteps)[::-1].copy()
+
+        self.tensor_format = tensor_format
         self.set_format(tensor_format=tensor_format)
 
-    def get_variance(self, t, num_inference_steps):
-        orig_t = self.config.timesteps // num_inference_steps * t
-        orig_prev_t = self.config.timesteps // num_inference_steps * (t - 1) if t > 0 else -1
-
-        alpha_prod_t = self.alphas_cumprod[orig_t]
-        alpha_prod_t_prev = self.alphas_cumprod[orig_prev_t] if orig_prev_t >= 0 else self.one
+    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.one
         beta_prod_t = 1 - alpha_prod_t
         beta_prod_t_prev = 1 - alpha_prod_t_prev
 
@@ -99,7 +103,22 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
 
         return variance
 
-    def step(self, residual, sample, t, num_inference_steps, eta, use_clipped_residual=False):
+    def set_timesteps(self, num_inference_steps):
+        self.num_inference_steps = num_inference_steps
+        self.timesteps = np.arange(0, self.config.timesteps, self.config.timesteps // self.num_inference_steps)[
+            ::-1
+        ].copy()
+        self.set_format(tensor_format=self.tensor_format)
+
+    def step(
+        self,
+        residual: Union[torch.FloatTensor, np.ndarray],
+        timestep: int,
+        sample: Union[torch.FloatTensor, np.ndarray],
+        eta,
+        use_clipped_residual=False,
+        generator=None,
+    ):
         # See formulas (12) and (16) of DDIM paper https://arxiv.org/pdf/2010.02502.pdf
         # Ideally, read DDIM paper in-detail understanding
 
@@ -111,13 +130,12 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         # - pred_sample_direction -> "direction pointingc to x_t"
         # - pred_prev_sample -> "x_t-1"
 
-        # 1. get actual t and t-1
-        orig_t = self.config.timesteps // num_inference_steps * t
-        orig_prev_t = self.config.timesteps // num_inference_steps * (t - 1) if t > 0 else -1
+        # 1. get previous step value (=t-1)
+        prev_timestep = timestep - self.config.timesteps // self.num_inference_steps
 
         # 2. compute alphas, betas
-        alpha_prod_t = self.alphas_cumprod[orig_t]
-        alpha_prod_t_prev = self.alphas_cumprod[orig_prev_t] if orig_prev_t >= 0 else self.one
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.one
         beta_prod_t = 1 - alpha_prod_t
 
         # 3. compute predicted original sample from predicted noise also called
@@ -130,7 +148,7 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
 
         # 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(t, num_inference_steps)
+        variance = self._get_variance(timestep, prev_timestep)
         std_dev_t = eta * variance ** (0.5)
 
         if use_clipped_residual:
@@ -141,9 +159,19 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         pred_sample_direction = (1 - alpha_prod_t_prev - std_dev_t**2) ** (0.5) * residual
 
         # 7. compute x_t without "random noise" of formula (12) from https://arxiv.org/pdf/2010.02502.pdf
-        pred_prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
+        prev_sample = alpha_prod_t_prev ** (0.5) * pred_original_sample + pred_sample_direction
 
-        return pred_prev_sample
+        if eta > 0:
+            device = residual.device if torch.is_tensor(residual) else "cpu"
+            noise = torch.randn(residual.shape, generator=generator).to(device)
+            variance = self._get_variance(timestep, prev_timestep) ** (0.5) * eta * noise
+
+            if not torch.is_tensor(residual):
+                variance = variance.numpy()
+
+            prev_sample = prev_sample + variance
+
+        return {"prev_sample": prev_sample}
 
     def add_noise(self, original_samples, noise, timesteps):
         sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
diff --git a/src/diffusers/schedulers/scheduling_ddpm.py b/src/diffusers/schedulers/scheduling_ddpm.py
index f80476b9c5..034a0d4280 100644
--- a/src/diffusers/schedulers/scheduling_ddpm.py
+++ b/src/diffusers/schedulers/scheduling_ddpm.py
@@ -15,8 +15,10 @@
 # DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim
 
 import math
+from typing import Union
 
 import numpy as np
+import torch
 
 from ..configuration_utils import ConfigMixin
 from .scheduling_utils import SchedulerMixin
@@ -112,7 +114,14 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
 
         return variance
 
-    def step(self, residual, sample, t, predict_epsilon=True):
+    def step(
+        self,
+        residual: Union[torch.FloatTensor, np.ndarray],
+        timestep: int,
+        sample: Union[torch.FloatTensor, np.ndarray],
+        predict_epsilon=True,
+    ):
+        t = timestep
         # 1. compute alphas, betas
         alpha_prod_t = self.alphas_cumprod[t]
         alpha_prod_t_prev = self.alphas_cumprod[t - 1] if t > 0 else self.one
@@ -139,7 +148,7 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         # See formula (7) from https://arxiv.org/pdf/2006.11239.pdf
         pred_prev_sample = pred_original_sample_coeff * pred_original_sample + current_sample_coeff * sample
 
-        return pred_prev_sample
+        return {"prev_sample": pred_prev_sample}
 
     def add_noise(self, original_samples, noise, timesteps):
         sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
diff --git a/src/diffusers/schedulers/scheduling_pndm.py b/src/diffusers/schedulers/scheduling_pndm.py
index 8533ad6cd7..3e398d53b1 100644
--- a/src/diffusers/schedulers/scheduling_pndm.py
+++ b/src/diffusers/schedulers/scheduling_pndm.py
@@ -15,8 +15,10 @@
 # DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim
 
 import math
+from typing import Union
 
 import numpy as np
+import torch
 
 from ..configuration_utils import ConfigMixin
 from .scheduling_utils import SchedulerMixin
@@ -126,7 +128,14 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
 
         raise ValueError(f"mode {self.mode} does not exist.")
 
-    def step_prk(self, residual, sample, t, num_inference_steps):
+    def step_prk(
+        self,
+        residual: Union[torch.FloatTensor, np.ndarray],
+        timestep: int,
+        sample: Union[torch.FloatTensor, np.ndarray],
+        num_inference_steps,
+    ):
+        t = timestep
         prk_time_steps = self.get_prk_time_steps(num_inference_steps)
 
         t_orig = prk_time_steps[t // 4 * 4]
@@ -147,9 +156,16 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
         # cur_sample should not be `None`
         cur_sample = self.cur_sample if self.cur_sample is not None else sample
 
-        return self.get_prev_sample(cur_sample, t_orig, t_orig_prev, residual)
+        return {"prev_sample": self.get_prev_sample(cur_sample, t_orig, t_orig_prev, residual)}
 
-    def step_plms(self, residual, sample, t, num_inference_steps):
+    def step_plms(
+        self,
+        residual: Union[torch.FloatTensor, np.ndarray],
+        timestep: int,
+        sample: Union[torch.FloatTensor, np.ndarray],
+        num_inference_steps,
+    ):
+        t = timestep
         if len(self.ets) < 3:
             raise ValueError(
                 f"{self.__class__} can only be run AFTER scheduler has been run "
@@ -166,7 +182,7 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
 
         residual = (1 / 24) * (55 * self.ets[-1] - 59 * self.ets[-2] + 37 * self.ets[-3] - 9 * self.ets[-4])
 
-        return self.get_prev_sample(sample, t_orig, t_orig_prev, residual)
+        return {"prev_sample": self.get_prev_sample(sample, t_orig, t_orig_prev, residual)}
 
     def get_prev_sample(self, sample, t_orig, t_orig_prev, residual):
         # See formula (9) of PNDM paper https://arxiv.org/pdf/2202.09778.pdf
diff --git a/tests/test_modeling_utils.py b/tests/test_modeling_utils.py
index a36946296e..1f694b458d 100755
--- a/tests/test_modeling_utils.py
+++ b/tests/test_modeling_utils.py
@@ -165,7 +165,7 @@ class ModelTesterMixin:
         # signature.parameters is an OrderedDict => so arg_names order is deterministic
         arg_names = [*signature.parameters.keys()]
 
-        expected_arg_names = ["sample", "step_value"]
+        expected_arg_names = ["sample", "timestep"]
         self.assertListEqual(arg_names[:2], expected_arg_names)
 
     def test_model_from_config(self):
@@ -248,7 +248,7 @@ class UnetModelTests(ModelTesterMixin, unittest.TestCase):
         noise = floats_tensor((batch_size, num_channels) + sizes).to(torch_device)
         time_step = torch.tensor([10]).to(torch_device)
 
-        return {"sample": noise, "step_value": time_step}
+        return {"sample": noise, "timestep": time_step}
 
     @property
     def input_shape(self):
@@ -323,7 +323,7 @@ class GlideSuperResUNetTests(ModelTesterMixin, unittest.TestCase):
         low_res = torch.randn((batch_size, 3) + low_res_size).to(torch_device)
         time_step = torch.tensor([10] * noise.shape[0], device=torch_device)
 
-        return {"sample": noise, "step_value": time_step, "low_res": low_res}
+        return {"sample": noise, "timestep": time_step, "low_res": low_res}
 
     @property
     def input_shape(self):
@@ -414,7 +414,7 @@ class GlideTextToImageUNetModelTests(ModelTesterMixin, unittest.TestCase):
         emb = torch.randn((batch_size, seq_len, transformer_dim)).to(torch_device)
         time_step = torch.tensor([10] * noise.shape[0], device=torch_device)
 
-        return {"sample": noise, "step_value": time_step, "transformer_out": emb}
+        return {"sample": noise, "timestep": time_step, "transformer_out": emb}
 
     @property
     def input_shape(self):
@@ -506,7 +506,7 @@ class UNetLDMModelTests(ModelTesterMixin, unittest.TestCase):
         noise = floats_tensor((batch_size, num_channels) + sizes).to(torch_device)
         time_step = torch.tensor([10]).to(torch_device)
 
-        return {"sample": noise, "step_value": time_step}
+        return {"sample": noise, "timestep": time_step}
 
     @property
     def input_shape(self):
@@ -601,7 +601,7 @@ class NCSNppModelTests(ModelTesterMixin, unittest.TestCase):
         noise = floats_tensor((batch_size, num_channels) + sizes).to(torch_device)
         time_step = torch.tensor(batch_size * [10]).to(torch_device)
 
-        return {"sample": noise, "step_value": time_step}
+        return {"sample": noise, "timestep": time_step}
 
     @property
     def input_shape(self):
@@ -899,8 +899,8 @@ class PipelineTesterMixin(unittest.TestCase):
         ddpm = DDPMPipeline.from_pretrained(model_path)
         ddpm_from_hub = DiffusionPipeline.from_pretrained(model_path)
 
-        ddpm.noise_scheduler.num_timesteps = 10
-        ddpm_from_hub.noise_scheduler.num_timesteps = 10
+        ddpm.scheduler.num_timesteps = 10
+        ddpm_from_hub.scheduler.num_timesteps = 10
 
         generator = torch.manual_seed(0)
 
@@ -915,10 +915,10 @@ class PipelineTesterMixin(unittest.TestCase):
         model_id = "fusing/ddpm-cifar10"
 
         unet = UNetUnconditionalModel.from_pretrained(model_id, ddpm=True)
-        noise_scheduler = DDPMScheduler.from_config(model_id)
-        noise_scheduler = noise_scheduler.set_format("pt")
+        scheduler = DDPMScheduler.from_config(model_id)
+        scheduler = scheduler.set_format("pt")
 
-        ddpm = DDPMPipeline(unet=unet, noise_scheduler=noise_scheduler)
+        ddpm = DDPMPipeline(unet=unet, scheduler=scheduler)
 
         generator = torch.manual_seed(0)
         image = ddpm(generator=generator)
@@ -936,13 +936,12 @@ class PipelineTesterMixin(unittest.TestCase):
         model_id = "fusing/ddpm-lsun-bedroom-ema"
 
         unet = UNetUnconditionalModel.from_pretrained(model_id, ddpm=True)
-        noise_scheduler = DDIMScheduler.from_config(model_id)
-        noise_scheduler = noise_scheduler.set_format("pt")
+        scheduler = DDIMScheduler.from_config(model_id)
 
-        ddpm = DDIMPipeline(unet=unet, noise_scheduler=noise_scheduler)
+        ddpm = DDIMPipeline(unet=unet, scheduler=scheduler)
 
         generator = torch.manual_seed(0)
-        image = ddpm(generator=generator)
+        image = ddpm(generator=generator)["sample"]
 
         image_slice = image[0, -1, -3:, -3:].cpu()
 
@@ -957,12 +956,12 @@ class PipelineTesterMixin(unittest.TestCase):
         model_id = "fusing/ddpm-cifar10"
 
         unet = UNetUnconditionalModel.from_pretrained(model_id, ddpm=True)
-        noise_scheduler = DDIMScheduler(tensor_format="pt")
+        scheduler = DDIMScheduler(tensor_format="pt")
 
-        ddim = DDIMPipeline(unet=unet, noise_scheduler=noise_scheduler)
+        ddim = DDIMPipeline(unet=unet, scheduler=scheduler)
 
         generator = torch.manual_seed(0)
-        image = ddim(generator=generator, eta=0.0)
+        image = ddim(generator=generator, eta=0.0)["sample"]
 
         image_slice = image[0, -1, -3:, -3:].cpu()
 
@@ -977,9 +976,9 @@ class PipelineTesterMixin(unittest.TestCase):
         model_id = "fusing/ddpm-cifar10"
 
         unet = UNetUnconditionalModel.from_pretrained(model_id, ddpm=True)
-        noise_scheduler = PNDMScheduler(tensor_format="pt")
+        scheduler = PNDMScheduler(tensor_format="pt")
 
-        pndm = PNDMPipeline(unet=unet, noise_scheduler=noise_scheduler)
+        pndm = PNDMPipeline(unet=unet, scheduler=scheduler)
         generator = torch.manual_seed(0)
         image = pndm(generator=generator)
 
@@ -1074,7 +1073,7 @@ class PipelineTesterMixin(unittest.TestCase):
         ldm = LatentDiffusionUncondPipeline.from_pretrained("fusing/latent-diffusion-celeba-256", ldm=True)
 
         generator = torch.manual_seed(0)
-        image = ldm(generator=generator, num_inference_steps=5)
+        image = ldm(generator=generator, num_inference_steps=5)["sample"]
 
         image_slice = image[0, -1, -3:, -3:].cpu()
 
diff --git a/tests/test_scheduler.py b/tests/test_scheduler.py
index 829383daba..0603fa5ddd 100755
--- a/tests/test_scheduler.py
+++ b/tests/test_scheduler.py
@@ -68,6 +68,8 @@ class SchedulerCommonTest(unittest.TestCase):
     def check_over_configs(self, time_step=0, **config):
         kwargs = dict(self.forward_default_kwargs)
 
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+
         for scheduler_class in self.scheduler_classes:
             scheduler_class = self.scheduler_classes[0]
             sample = self.dummy_sample
@@ -80,8 +82,14 @@ class SchedulerCommonTest(unittest.TestCase):
                 scheduler.save_config(tmpdirname)
                 new_scheduler = scheduler_class.from_config(tmpdirname)
 
-            output = scheduler.step(residual, sample, time_step, **kwargs)
-            new_output = new_scheduler.step(residual, sample, time_step, **kwargs)
+            if num_inference_steps is not None and hasattr(scheduler, "set_timesteps"):
+                scheduler.set_timesteps(num_inference_steps)
+                new_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
+
+            output = scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
+            new_output = new_scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
 
             assert np.sum(np.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
 
@@ -89,6 +97,8 @@ class SchedulerCommonTest(unittest.TestCase):
         kwargs = dict(self.forward_default_kwargs)
         kwargs.update(forward_kwargs)
 
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+
         for scheduler_class in self.scheduler_classes:
             sample = self.dummy_sample
             residual = 0.1 * sample
@@ -101,14 +111,24 @@ class SchedulerCommonTest(unittest.TestCase):
                 scheduler.save_config(tmpdirname)
                 new_scheduler = scheduler_class.from_config(tmpdirname)
 
-            output = scheduler.step(residual, sample, time_step, **kwargs)
-            new_output = new_scheduler.step(residual, sample, time_step, **kwargs)
+            if num_inference_steps is not None and hasattr(scheduler, "set_timesteps"):
+                scheduler.set_timesteps(num_inference_steps)
+                new_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
+
+            torch.manual_seed(0)
+            output = scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
+            torch.manual_seed(0)
+            new_output = new_scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
 
             assert np.sum(np.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
 
     def test_from_pretrained_save_pretrained(self):
         kwargs = dict(self.forward_default_kwargs)
 
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+
         for scheduler_class in self.scheduler_classes:
             sample = self.dummy_sample
             residual = 0.1 * sample
@@ -120,14 +140,22 @@ class SchedulerCommonTest(unittest.TestCase):
                 scheduler.save_config(tmpdirname)
                 new_scheduler = scheduler_class.from_config(tmpdirname)
 
-            output = scheduler.step(residual, sample, 1, **kwargs)
-            new_output = new_scheduler.step(residual, sample, 1, **kwargs)
+            if num_inference_steps is not None and hasattr(scheduler, "set_timesteps"):
+                scheduler.set_timesteps(num_inference_steps)
+                new_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
+
+            output = scheduler.step(residual, 1, sample, **kwargs)["prev_sample"]
+            new_output = new_scheduler.step(residual, 1, sample, **kwargs)["prev_sample"]
 
             assert np.sum(np.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
 
     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)
@@ -135,8 +163,13 @@ class SchedulerCommonTest(unittest.TestCase):
             sample = self.dummy_sample
             residual = 0.1 * sample
 
-            output_0 = scheduler.step(residual, sample, 0, **kwargs)
-            output_1 = scheduler.step(residual, sample, 1, **kwargs)
+            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
+
+            output_0 = scheduler.step(residual, 0, sample, **kwargs)["prev_sample"]
+            output_1 = scheduler.step(residual, 1, sample, **kwargs)["prev_sample"]
 
             self.assertEqual(output_0.shape, sample.shape)
             self.assertEqual(output_0.shape, output_1.shape)
@@ -144,6 +177,8 @@ class SchedulerCommonTest(unittest.TestCase):
     def test_pytorch_equal_numpy(self):
         kwargs = dict(self.forward_default_kwargs)
 
+        num_inference_steps = kwargs.pop("num_inference_steps", None)
+
         for scheduler_class in self.scheduler_classes:
             sample = self.dummy_sample
             residual = 0.1 * sample
@@ -156,8 +191,14 @@ class SchedulerCommonTest(unittest.TestCase):
 
             scheduler_pt = scheduler_class(tensor_format="pt", **scheduler_config)
 
-            output = scheduler.step(residual, sample, 1, **kwargs)
-            output_pt = scheduler_pt.step(residual_pt, sample_pt, 1, **kwargs)
+            if num_inference_steps is not None and hasattr(scheduler, "set_timesteps"):
+                scheduler.set_timesteps(num_inference_steps)
+                scheduler_pt.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
+
+            output = scheduler.step(residual, 1, sample, **kwargs)["prev_sample"]
+            output_pt = scheduler_pt.step(residual_pt, 1, sample_pt, **kwargs)["prev_sample"]
 
             assert np.sum(np.abs(output - output_pt.numpy())) < 1e-4, "Scheduler outputs are not identical"
 
@@ -226,7 +267,7 @@ class DDPMSchedulerTest(SchedulerCommonTest):
             residual = model(sample, t)
 
             # 2. predict previous mean of sample x_t-1
-            pred_prev_sample = scheduler.step(residual, sample, t)
+            pred_prev_sample = scheduler.step(residual, t, sample)["prev_sample"]
 
             if t > 0:
                 noise = self.dummy_sample_deter
@@ -243,7 +284,7 @@ class DDPMSchedulerTest(SchedulerCommonTest):
 
 class DDIMSchedulerTest(SchedulerCommonTest):
     scheduler_classes = (DDIMScheduler,)
-    forward_default_kwargs = (("num_inference_steps", 50), ("eta", 0.0))
+    forward_default_kwargs = (("eta", 0.0), ("num_inference_steps", 50))
 
     def get_scheduler_config(self, **kwargs):
         config = {
@@ -258,7 +299,7 @@ class DDIMSchedulerTest(SchedulerCommonTest):
         return config
 
     def test_timesteps(self):
-        for timesteps in [1, 5, 100, 1000]:
+        for timesteps in [100, 500, 1000]:
             self.check_over_configs(timesteps=timesteps)
 
     def test_betas(self):
@@ -279,7 +320,7 @@ class DDIMSchedulerTest(SchedulerCommonTest):
 
     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)
+            self.check_over_forward(num_inference_steps=num_inference_steps)
 
     def test_eta(self):
         for t, eta in zip([1, 10, 49], [0.0, 0.5, 1.0]):
@@ -290,43 +331,34 @@ class DDIMSchedulerTest(SchedulerCommonTest):
         scheduler_config = self.get_scheduler_config()
         scheduler = scheduler_class(**scheduler_config)
 
-        assert np.sum(np.abs(scheduler.get_variance(0, 50) - 0.0)) < 1e-5
-        assert np.sum(np.abs(scheduler.get_variance(21, 50) - 0.14771)) < 1e-5
-        assert np.sum(np.abs(scheduler.get_variance(49, 50) - 0.32460)) < 1e-5
-        assert np.sum(np.abs(scheduler.get_variance(0, 1000) - 0.0)) < 1e-5
-        assert np.sum(np.abs(scheduler.get_variance(487, 1000) - 0.00979)) < 1e-5
-        assert np.sum(np.abs(scheduler.get_variance(999, 1000) - 0.02)) < 1e-5
+        assert np.sum(np.abs(scheduler._get_variance(0, 0) - 0.0)) < 1e-5
+        assert np.sum(np.abs(scheduler._get_variance(420, 400) - 0.14771)) < 1e-5
+        assert np.sum(np.abs(scheduler._get_variance(980, 960) - 0.32460)) < 1e-5
+        assert np.sum(np.abs(scheduler._get_variance(0, 0) - 0.0)) < 1e-5
+        assert np.sum(np.abs(scheduler._get_variance(487, 486) - 0.00979)) < 1e-5
+        assert np.sum(np.abs(scheduler._get_variance(999, 998) - 0.02)) < 1e-5
 
     def test_full_loop_no_noise(self):
         scheduler_class = self.scheduler_classes[0]
         scheduler_config = self.get_scheduler_config()
         scheduler = scheduler_class(**scheduler_config)
 
-        num_inference_steps, eta = 10, 0.1
-        num_trained_timesteps = len(scheduler)
-
-        inference_step_times = range(0, num_trained_timesteps, num_trained_timesteps // num_inference_steps)
+        num_inference_steps, eta = 10, 0.0
 
         model = self.dummy_model()
         sample = self.dummy_sample_deter
 
-        for t in reversed(range(num_inference_steps)):
-            residual = model(sample, inference_step_times[t])
+        scheduler.set_timesteps(num_inference_steps)
+        for t in scheduler.timesteps:
+            residual = model(sample, t)
 
-            pred_prev_sample = scheduler.step(residual, sample, t, num_inference_steps, eta)
-
-            variance = 0
-            if eta > 0:
-                noise = self.dummy_sample_deter
-                variance = scheduler.get_variance(t, num_inference_steps) ** (0.5) * eta * noise
-
-            sample = pred_prev_sample + variance
+            sample = scheduler.step(residual, t, sample, eta)["prev_sample"]
 
         result_sum = np.sum(np.abs(sample))
         result_mean = np.mean(np.abs(sample))
 
-        assert abs(result_sum.item() - 270.6214) < 1e-2
-        assert abs(result_mean.item() - 0.3524) < 1e-3
+        assert abs(result_sum.item() - 172.0067) < 1e-2
+        assert abs(result_mean.item() - 0.223967) < 1e-3
 
 
 class PNDMSchedulerTest(SchedulerCommonTest):
@@ -365,8 +397,8 @@ class PNDMSchedulerTest(SchedulerCommonTest):
                 new_scheduler.ets = dummy_past_residuals[:]
                 new_scheduler.set_plms_mode()
 
-            output = scheduler.step(residual, sample, time_step, **kwargs)
-            new_output = new_scheduler.step(residual, sample, time_step, **kwargs)
+            output = scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
+            new_output = new_scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
 
             assert np.sum(np.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
 
@@ -392,8 +424,8 @@ class PNDMSchedulerTest(SchedulerCommonTest):
                 new_scheduler.ets = dummy_past_residuals[:]
                 new_scheduler.set_plms_mode()
 
-            output = scheduler.step(residual, sample, time_step, **kwargs)
-            new_output = new_scheduler.step(residual, sample, time_step, **kwargs)
+            output = scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
+            new_output = new_scheduler.step(residual, time_step, sample, **kwargs)["prev_sample"]
 
             assert np.sum(np.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
 
@@ -445,7 +477,7 @@ class PNDMSchedulerTest(SchedulerCommonTest):
 
             scheduler.set_plms_mode()
 
-            scheduler.step(self.dummy_sample, self.dummy_sample, 1, 50)
+            scheduler.step(self.dummy_sample, 1, self.dummy_sample, 50)["prev_sample"]
 
     def test_full_loop_no_noise(self):
         scheduler_class = self.scheduler_classes[0]
@@ -461,14 +493,14 @@ class PNDMSchedulerTest(SchedulerCommonTest):
             t_orig = prk_time_steps[t]
             residual = model(sample, t_orig)
 
-            sample = scheduler.step_prk(residual, sample, t, num_inference_steps)
+            sample = scheduler.step_prk(residual, t, sample, num_inference_steps)["prev_sample"]
 
         timesteps = scheduler.get_time_steps(num_inference_steps)
         for t in range(len(timesteps)):
             t_orig = timesteps[t]
             residual = model(sample, t_orig)
 
-            sample = scheduler.step_plms(residual, sample, t, num_inference_steps)
+            sample = scheduler.step_plms(residual, t, sample, num_inference_steps)["prev_sample"]
 
         result_sum = np.sum(np.abs(sample))
         result_mean = np.mean(np.abs(sample))