diff --git a/src/diffusers/__init__.py b/src/diffusers/__init__.py
index acdddaac4d26..802fa9a903ac 100644
--- a/src/diffusers/__init__.py
+++ b/src/diffusers/__init__.py
@@ -31,6 +31,7 @@
     from .pipeline_utils import DiffusionPipeline
     from .pipelines import DDIMPipeline, DDPMPipeline, KarrasVePipeline, LDMPipeline, PNDMPipeline, ScoreSdeVePipeline
     from .schedulers import (
+        BaseScheduler,
         DDIMScheduler,
         DDPMScheduler,
         KarrasVeScheduler,
diff --git a/src/diffusers/dependency_versions_table.py b/src/diffusers/dependency_versions_table.py
index 09a7baad560d..82ca5dbb6f56 100644
--- a/src/diffusers/dependency_versions_table.py
+++ b/src/diffusers/dependency_versions_table.py
@@ -17,7 +17,6 @@
     "jaxlib": "jaxlib>=0.1.65,<=0.3.6",
     "modelcards": "modelcards>=0.1.4",
     "numpy": "numpy",
-    "onnxruntime": "onnxruntime",
     "onnxruntime-gpu": "onnxruntime-gpu",
     "pytest": "pytest",
     "pytest-timeout": "pytest-timeout",
diff --git a/src/diffusers/pipeline_utils.py b/src/diffusers/pipeline_utils.py
index fb8801bc959a..a04ee652c5a7 100644
--- a/src/diffusers/pipeline_utils.py
+++ b/src/diffusers/pipeline_utils.py
@@ -43,6 +43,7 @@
 LOADABLE_CLASSES = {
     "diffusers": {
         "ModelMixin": ["save_pretrained", "from_pretrained"],
+        "BaseScheduler": ["save_config", "from_config"],
         "SchedulerMixin": ["save_config", "from_config"],
         "DiffusionPipeline": ["save_pretrained", "from_pretrained"],
         "OnnxRuntimeModel": ["save_pretrained", "from_pretrained"],
diff --git a/src/diffusers/pipelines/ddim/pipeline_ddim.py b/src/diffusers/pipelines/ddim/pipeline_ddim.py
index 74607fe87a3d..58808e5db0cf 100644
--- a/src/diffusers/pipelines/ddim/pipeline_ddim.py
+++ b/src/diffusers/pipelines/ddim/pipeline_ddim.py
@@ -82,14 +82,15 @@ def __call__(
         # set step values
         self.scheduler.set_timesteps(num_inference_steps)
 
-        for t in self.progress_bar(self.scheduler.timesteps):
+        for step in self.progress_bar(self.scheduler.timesteps):
             # 1. predict noise model_output
+            t = self.scheduler.get_noise_condition(step)
             model_output = self.unet(image, t).sample
 
             # 2. predict previous mean of image x_t-1 and add variance depending on eta
             # eta corresponds to η in paper and should be between [0, 1]
             # do x_t -> x_t-1
-            image = self.scheduler.step(model_output, t, image, eta).prev_sample
+            image = self.scheduler.step(model_output, step, image, eta).prev_sample
 
         image = (image / 2 + 0.5).clamp(0, 1)
         image = image.cpu().permute(0, 2, 3, 1).numpy()
diff --git a/src/diffusers/pipelines/ddpm/pipeline_ddpm.py b/src/diffusers/pipelines/ddpm/pipeline_ddpm.py
index aae29737aae3..4258e79681a2 100644
--- a/src/diffusers/pipelines/ddpm/pipeline_ddpm.py
+++ b/src/diffusers/pipelines/ddpm/pipeline_ddpm.py
@@ -75,12 +75,13 @@ def __call__(
         # set step values
         self.scheduler.set_timesteps(1000)
 
-        for t in self.progress_bar(self.scheduler.timesteps):
+        for step in self.progress_bar(self.scheduler.timesteps):
             # 1. predict noise model_output
+            t = self.scheduler.get_noise_condition(step)
             model_output = self.unet(image, t).sample
 
             # 2. compute previous image: x_t -> t_t-1
-            image = self.scheduler.step(model_output, t, image, generator=generator).prev_sample
+            image = self.scheduler.step(model_output, step, image, generator=generator).prev_sample
 
         image = (image / 2 + 0.5).clamp(0, 1)
         image = image.cpu().permute(0, 2, 3, 1).numpy()
diff --git a/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py b/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py
index 556e4211892b..63e27ef23707 100644
--- a/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py
+++ b/src/diffusers/pipelines/latent_diffusion/pipeline_latent_diffusion.py
@@ -117,6 +117,7 @@ def __call__(
             generator=generator,
         )
         latents = latents.to(self.device)
+        latents = self.scheduler.scale_initial_noise(latents)
 
         self.scheduler.set_timesteps(num_inference_steps)
 
@@ -127,7 +128,7 @@ def __call__(
         if accepts_eta:
             extra_kwargs["eta"] = eta
 
-        for t in self.progress_bar(self.scheduler.timesteps):
+        for step in self.progress_bar(self.scheduler.timesteps):
             if guidance_scale == 1.0:
                 # guidance_scale of 1 means no guidance
                 latents_input = latents
@@ -140,6 +141,8 @@ def __call__(
                 context = torch.cat([uncond_embeddings, text_embeddings])
 
             # predict the noise residual
+            latents_input = self.scheduler.scale_model_input(latents_input, step)
+            t = self.scheduler.get_noise_condition(step)
             noise_pred = self.unet(latents_input, t, encoder_hidden_states=context).sample
             # perform guidance
             if guidance_scale != 1.0:
@@ -147,7 +150,7 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_prediction_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            latents = self.scheduler.step(noise_pred, t, latents, **extra_kwargs).prev_sample
+            latents = self.scheduler.step(noise_pred, step, latents, **extra_kwargs).prev_sample
 
         # scale and decode the image latents with vae
         latents = 1 / 0.18215 * latents
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 ef82abb7e6cb..377d98e5338b 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
@@ -63,6 +63,7 @@ def __call__(
             generator=generator,
         )
         latents = latents.to(self.device)
+        latents = self.scheduler.scale_initial_noise(latents)
 
         self.scheduler.set_timesteps(num_inference_steps)
 
@@ -73,11 +74,13 @@ def __call__(
         if accepts_eta:
             extra_kwargs["eta"] = eta
 
-        for t in self.progress_bar(self.scheduler.timesteps):
+        for step in self.progress_bar(self.scheduler.timesteps):
             # predict the noise residual
+            latents = self.scheduler.scale_model_input(latents, step)
+            t = self.scheduler.get_noise_condition(step)
             noise_prediction = self.unet(latents, t).sample
             # compute the previous noisy sample x_t -> x_t-1
-            latents = self.scheduler.step(noise_prediction, t, latents, **extra_kwargs).prev_sample
+            latents = self.scheduler.step(noise_prediction, step, latents, **extra_kwargs).prev_sample
 
         # decode the image latents with the VAE
         image = self.vqvae.decode(latents).sample
diff --git a/src/diffusers/pipelines/pndm/pipeline_pndm.py b/src/diffusers/pipelines/pndm/pipeline_pndm.py
index f360da09ac94..29aa5435ec62 100644
--- a/src/diffusers/pipelines/pndm/pipeline_pndm.py
+++ b/src/diffusers/pipelines/pndm/pipeline_pndm.py
@@ -79,12 +79,14 @@ def __call__(
             generator=generator,
         )
         image = image.to(self.device)
+        image = self.scheduler.scale_initial_noise(image)
 
         self.scheduler.set_timesteps(num_inference_steps)
-        for t in self.progress_bar(self.scheduler.timesteps):
+        for step in self.progress_bar(self.scheduler.timesteps):
+            t = self.scheduler.get_noise_condition(step)
             model_output = self.unet(image, t).sample
 
-            image = self.scheduler.step(model_output, t, image).prev_sample
+            image = self.scheduler.step(model_output, step, image).prev_sample
 
         image = (image / 2 + 0.5).clamp(0, 1)
         image = image.cpu().permute(0, 2, 3, 1).numpy()
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
index 77f25ef1b9c5..62ea4247bff5 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
@@ -46,6 +46,14 @@ class StableDiffusionPipeline(DiffusionPipeline):
             Model that extracts features from generated images to be used as inputs for the `safety_checker`.
     """
 
+    vae: AutoencoderKL
+    text_encoder: CLIPTextModel
+    tokenizer: CLIPTokenizer
+    unet: UNet2DConditionModel
+    scheduler: Union[DDIMScheduler, PNDMScheduler, LMSDiscreteScheduler]
+    safety_checker: StableDiffusionSafetyChecker
+    feature_extractor: CLIPFeatureExtractor
+
     def __init__(
         self,
         vae: AutoencoderKL,
@@ -230,14 +238,11 @@ def __call__(
             if latents.shape != latents_shape:
                 raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {latents_shape}")
         latents = latents.to(self.device)
+        latents = self.scheduler.scale_initial_noise(latents)
 
         # set timesteps
         self.scheduler.set_timesteps(num_inference_steps)
 
-        # if we use LMSDiscreteScheduler, let's make sure latents are multiplied by sigmas
-        if isinstance(self.scheduler, LMSDiscreteScheduler):
-            latents = latents * self.scheduler.sigmas[0]
-
         # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
         # eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
         # eta corresponds to η in DDIM paper: https://arxiv.org/abs/2010.02502
@@ -247,13 +252,11 @@ def __call__(
         if accepts_eta:
             extra_step_kwargs["eta"] = eta
 
-        for i, t in enumerate(self.progress_bar(self.scheduler.timesteps)):
+        for step in self.progress_bar(self.scheduler.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
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[i]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, step)
+            t = self.scheduler.get_noise_condition(step)
 
             # predict the noise residual
             noise_pred = self.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample
@@ -264,10 +267,7 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, i, latents, **extra_step_kwargs).prev_sample
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
+            latents = self.scheduler.step(noise_pred, step, latents, **extra_step_kwargs).prev_sample
 
         # scale and decode the image latents with vae
         latents = 1 / 0.18215 * latents
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
index f2ccee71c024..c9c8f4628901 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
@@ -206,13 +206,7 @@ def __call__(
         offset = self.scheduler.config.get("steps_offset", 0)
         init_timestep = int(num_inference_steps * strength) + offset
         init_timestep = min(init_timestep, num_inference_steps)
-        if isinstance(self.scheduler, LMSDiscreteScheduler):
-            timesteps = torch.tensor(
-                [num_inference_steps - init_timestep] * batch_size, dtype=torch.long, device=self.device
-            )
-        else:
-            timesteps = self.scheduler.timesteps[-init_timestep]
-            timesteps = torch.tensor([timesteps] * batch_size, dtype=torch.long, device=self.device)
+        timesteps = torch.tensor([init_timestep - 1] * batch_size, dtype=torch.long, device=self.device)
 
         # add noise to latents using the timesteps
         noise = torch.randn(init_latents.shape, generator=generator, device=self.device)
@@ -265,17 +259,11 @@ def __call__(
         latents = init_latents
 
         t_start = max(num_inference_steps - init_timestep + offset, 0)
-        for i, t in enumerate(self.progress_bar(self.scheduler.timesteps[t_start:])):
-            t_index = t_start + i
-
+        for step in self.progress_bar(self.scheduler.timesteps[t_start:]):
             # expand the latents if we are doing classifier free guidance
             latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
-
-            # if we use LMSDiscreteScheduler, let's make sure latents are multiplied by sigmas
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[t_index]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, step)
+            t = self.scheduler.get_noise_condition(step)
 
             # predict the noise residual
             noise_pred = self.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample
@@ -286,10 +274,7 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, t_index, latents, **extra_step_kwargs).prev_sample
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
+            latents = self.scheduler.step(noise_pred, step, latents, **extra_step_kwargs).prev_sample
 
         # scale and decode the image latents with vae
         latents = 1 / 0.18215 * latents
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
index a95f9152279a..6deb6a2a3285 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
@@ -6,7 +6,6 @@
 import torch
 
 import PIL
-from tqdm.auto import tqdm
 from transformers import CLIPFeatureExtractor, CLIPTextModel, CLIPTokenizer
 
 from ...configuration_utils import FrozenDict
@@ -240,13 +239,7 @@ def __call__(
         offset = self.scheduler.config.get("steps_offset", 0)
         init_timestep = int(num_inference_steps * strength) + offset
         init_timestep = min(init_timestep, num_inference_steps)
-        if isinstance(self.scheduler, LMSDiscreteScheduler):
-            timesteps = torch.tensor(
-                [num_inference_steps - init_timestep] * batch_size, dtype=torch.long, device=self.device
-            )
-        else:
-            timesteps = self.scheduler.timesteps[-init_timestep]
-            timesteps = torch.tensor([timesteps] * batch_size, dtype=torch.long, device=self.device)
+        timesteps = torch.tensor([init_timestep - 1] * batch_size, dtype=torch.long, device=self.device)
 
         # add noise to latents using the timesteps
         noise = torch.randn(init_latents.shape, generator=generator, device=self.device)
@@ -298,14 +291,11 @@ def __call__(
 
         latents = init_latents
         t_start = max(num_inference_steps - init_timestep + offset, 0)
-        for i, t in tqdm(enumerate(self.scheduler.timesteps[t_start:])):
-            t_index = t_start + i
+        for step in self.progress_bar(self.scheduler.timesteps[t_start:]):
             # expand the latents if we are doing classifier free guidance
             latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[t_index]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, step)
+            t = self.scheduler.get_noise_condition(step)
 
             # predict the noise residual
             noise_pred = self.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample
@@ -316,14 +306,9 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, t_index, latents, **extra_step_kwargs).prev_sample
-                # masking
-                init_latents_proper = self.scheduler.add_noise(init_latents_orig, noise, torch.LongTensor([t_index]))
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
-                # masking
-                init_latents_proper = self.scheduler.add_noise(init_latents_orig, noise, torch.LongTensor([t]))
+            latents = self.scheduler.step(noise_pred, step, latents, **extra_step_kwargs).prev_sample
+            # masking
+            init_latents_proper = self.scheduler.add_noise(init_latents_orig, noise, torch.tensor(step))
 
             latents = (init_latents_proper * mask) + (latents * (1 - mask))
 
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
index 07e9c1d9acd6..6adc5e23e78d 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
@@ -109,6 +109,7 @@ def __call__(
             latents = np.random.randn(*latents_shape).astype(np.float32)
         elif latents.shape != latents_shape:
             raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {latents_shape}")
+        latents = self.scheduler.scale_initial_noise(latents)
 
         # set timesteps
         self.scheduler.set_timesteps(num_inference_steps)
@@ -126,13 +127,11 @@ def __call__(
         if accepts_eta:
             extra_step_kwargs["eta"] = eta
 
-        for i, t in enumerate(self.progress_bar(self.scheduler.timesteps)):
+        for step in self.progress_bar(self.scheduler.timesteps):
             # expand the latents if we are doing classifier free guidance
             latent_model_input = np.concatenate([latents] * 2) if do_classifier_free_guidance else latents
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[i]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, step)
+            t = self.scheduler.get_noise_condition(step)
 
             # predict the noise residual
             noise_pred = self.unet(
@@ -146,10 +145,7 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, i, latents, **extra_step_kwargs).prev_sample
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
+            latents = self.scheduler.step(noise_pred, step, latents, **extra_step_kwargs).prev_sample
 
         # scale and decode the image latents with vae
         latents = 1 / 0.18215 * latents
diff --git a/src/diffusers/schedulers/__init__.py b/src/diffusers/schedulers/__init__.py
index 495f30d9fabd..2828753e72d9 100644
--- a/src/diffusers/schedulers/__init__.py
+++ b/src/diffusers/schedulers/__init__.py
@@ -23,7 +23,7 @@
     from .scheduling_pndm import PNDMScheduler
     from .scheduling_sde_ve import ScoreSdeVeScheduler
     from .scheduling_sde_vp import ScoreSdeVpScheduler
-    from .scheduling_utils import SchedulerMixin
+    from .scheduling_utils import BaseScheduler, SchedulerMixin
 else:
     from ..utils.dummy_pt_objects import *  # noqa F403
 
diff --git a/src/diffusers/schedulers/scheduling_ddim.py b/src/diffusers/schedulers/scheduling_ddim.py
index 0d9e285e054e..61c386ac7a06 100644
--- a/src/diffusers/schedulers/scheduling_ddim.py
+++ b/src/diffusers/schedulers/scheduling_ddim.py
@@ -25,7 +25,7 @@
 
 from ..configuration_utils import ConfigMixin, register_to_config
 from ..utils import BaseOutput
-from .scheduling_utils import SchedulerMixin
+from .scheduling_utils import BaseScheduler
 
 
 @dataclass
@@ -75,7 +75,7 @@ def alpha_bar(time_step):
     return torch.tensor(betas)
 
 
-class DDIMScheduler(SchedulerMixin, ConfigMixin):
+class DDIMScheduler(BaseScheduler, ConfigMixin):
     """
     Denoising diffusion implicit models is a scheduler that extends the denoising procedure introduced in denoising
     diffusion probabilistic models (DDPMs) with non-Markovian guidance.
@@ -155,7 +155,8 @@ def __init__(
 
         # setable values
         self.num_inference_steps = None
-        self.timesteps = np.arange(0, num_train_timesteps)[::-1]
+        self.schedule = np.arange(0, num_train_timesteps)
+        self.timesteps = self.schedule[::-1]
 
     def _get_variance(self, timestep, prev_timestep):
         alpha_prod_t = self.alphas_cumprod[timestep]
@@ -167,6 +168,12 @@ def _get_variance(self, timestep, prev_timestep):
 
         return variance
 
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for a model.
+        """
+        return self.schedule[step]
+
     def set_timesteps(self, num_inference_steps: int, **kwargs):
         """
         Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
@@ -191,8 +198,10 @@ def set_timesteps(self, num_inference_steps: int, **kwargs):
         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
-        self.timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1]
-        self.timesteps += offset
+        self.schedule = (np.arange(0, num_inference_steps) * step_ratio).round().copy()
+        self.schedule += offset
+
+        self.timesteps = np.arange(0, num_inference_steps)[::-1].copy()
 
     def step(
         self,
@@ -240,6 +249,8 @@ def step(
         # - pred_sample_direction -> "direction pointing to x_t"
         # - pred_prev_sample -> "x_t-1"
 
+        timestep = self.schedule[timestep]
+
         # 1. get previous step value (=t-1)
         prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps
 
@@ -295,7 +306,7 @@ def add_noise(
 
         if timesteps.device != original_samples.device:
             timesteps = timesteps.to(original_samples.device)
-
+        timesteps = self.schedule[timesteps]
         sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
         sqrt_alpha_prod = sqrt_alpha_prod.flatten()
         while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
diff --git a/src/diffusers/schedulers/scheduling_ddpm.py b/src/diffusers/schedulers/scheduling_ddpm.py
index cc17cee4c810..0e289e131dbb 100644
--- a/src/diffusers/schedulers/scheduling_ddpm.py
+++ b/src/diffusers/schedulers/scheduling_ddpm.py
@@ -24,7 +24,7 @@
 
 from ..configuration_utils import ConfigMixin, register_to_config
 from ..utils import BaseOutput
-from .scheduling_utils import SchedulerMixin
+from .scheduling_utils import BaseScheduler
 
 
 @dataclass
@@ -74,7 +74,7 @@ def alpha_bar(time_step):
     return torch.tensor(betas, dtype=torch.float32)
 
 
-class DDPMScheduler(SchedulerMixin, ConfigMixin):
+class DDPMScheduler(BaseScheduler, ConfigMixin):
     """
     Denoising diffusion probabilistic models (DDPMs) explores the connections between denoising score matching and
     Langevin dynamics sampling.
@@ -143,10 +143,17 @@ def __init__(
 
         # setable values
         self.num_inference_steps = None
-        self.timesteps = np.arange(0, num_train_timesteps)[::-1]
+        self.schedule = np.arange(0, num_train_timesteps)
+        self.timesteps = self.schedule[::-1]
 
         self.variance_type = variance_type
 
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for a model.
+        """
+        return self.schedule[step]
+
     def set_timesteps(self, num_inference_steps: int):
         """
         Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
@@ -223,7 +230,7 @@ def step(
             returning a tuple, the first element is the sample tensor.
 
         """
-        t = timestep
+        t = self.schedule[timestep]
 
         if model_output.shape[1] == sample.shape[1] * 2 and self.variance_type in ["learned", "learned_range"]:
             model_output, predicted_variance = torch.split(model_output, sample.shape[1], dim=1)
@@ -281,8 +288,7 @@ def add_noise(
             self.alphas_cumprod = self.alphas_cumprod.to(original_samples.device)
 
         if timesteps.device != original_samples.device:
-            timesteps = timesteps.to(original_samples.device)
-
+            timesteps = self.schedule[timesteps].to(original_samples.device)
         sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
         sqrt_alpha_prod = sqrt_alpha_prod.flatten()
         while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
diff --git a/src/diffusers/schedulers/scheduling_karras_ve.py b/src/diffusers/schedulers/scheduling_karras_ve.py
index e6e5300e73e7..90246009fa5e 100644
--- a/src/diffusers/schedulers/scheduling_karras_ve.py
+++ b/src/diffusers/schedulers/scheduling_karras_ve.py
@@ -22,7 +22,7 @@
 
 from ..configuration_utils import ConfigMixin, register_to_config
 from ..utils import BaseOutput
-from .scheduling_utils import SchedulerMixin
+from .scheduling_utils import BaseScheduler
 
 
 @dataclass
@@ -46,7 +46,7 @@ class KarrasVeOutput(BaseOutput):
     pred_original_sample: Optional[torch.FloatTensor] = None
 
 
-class KarrasVeScheduler(SchedulerMixin, ConfigMixin):
+class KarrasVeScheduler(BaseScheduler, ConfigMixin):
     """
     Stochastic sampling from Karras et al. [1] tailored to the Variance-Expanding (VE) models [2]. Use Algorithm 2 and
     the VE column of Table 1 from [1] for reference.
@@ -101,6 +101,12 @@ def __init__(
         self.timesteps: np.ndarray = None
         self.schedule: torch.FloatTensor = None  # sigma(t_i)
 
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for the model.
+        """
+        return self.schedule[step]
+
     def set_timesteps(self, num_inference_steps: int):
         """
         Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference.
diff --git a/src/diffusers/schedulers/scheduling_lms_discrete.py b/src/diffusers/schedulers/scheduling_lms_discrete.py
index 6d8db7682db5..a09fed168f2e 100644
--- a/src/diffusers/schedulers/scheduling_lms_discrete.py
+++ b/src/diffusers/schedulers/scheduling_lms_discrete.py
@@ -23,7 +23,7 @@
 
 from ..configuration_utils import ConfigMixin, register_to_config
 from ..utils import BaseOutput
-from .scheduling_utils import SchedulerMixin
+from .scheduling_utils import BaseScheduler
 
 
 @dataclass
@@ -44,7 +44,7 @@ class LMSDiscreteSchedulerOutput(BaseOutput):
     pred_original_sample: Optional[torch.FloatTensor] = None
 
 
-class LMSDiscreteScheduler(SchedulerMixin, ConfigMixin):
+class LMSDiscreteScheduler(BaseScheduler, ConfigMixin):
     """
     Linear Multistep Scheduler for discrete beta schedules. Based on the original k-diffusion implementation by
     Katherine Crowson:
@@ -99,13 +99,36 @@ def __init__(
         self.alphas = 1.0 - self.betas
         self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
 
-        self.sigmas = ((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5
+        sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
+        sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32)
+        self.sigmas = torch.from_numpy(sigmas)
 
         # setable values
         self.num_inference_steps = None
-        self.timesteps = np.arange(0, num_train_timesteps)[::-1]  # to be consistent has to be smaller than sigmas by 1
+        self.timesteps = np.arange(0, num_train_timesteps)[::-1].copy()
+        schedule = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)
+        self.schedule = torch.from_numpy(schedule)
         self.derivatives = []
 
+    def scale_initial_noise(self, noise: torch.FloatTensor):
+        """
+        Scales the initial noise to the correct range for the scheduler.
+        """
+        return noise * self.sigmas[0]
+
+    def scale_model_input(self, sample: torch.FloatTensor, step: int):
+        """
+        Scales the model input (`sample`) to the correct range for the scheduler.
+        """
+        sigma = self.sigmas[self.num_inference_steps - step - 1]
+        return sample / ((sigma**2 + 1) ** 0.5)
+
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for a model.
+        """
+        return self.schedule[step]
+
     def get_lms_coefficient(self, order, t, current_order):
         """
         Compute a linear multistep coefficient.
@@ -137,17 +160,15 @@ def set_timesteps(self, num_inference_steps: int):
                 the number of diffusion steps used when generating samples with a pre-trained model.
         """
         self.num_inference_steps = num_inference_steps
-        timesteps = np.linspace(self.config.num_train_timesteps - 1, 0, num_inference_steps, dtype=float)
+        self.timesteps = np.arange(0, num_inference_steps)[::-1].copy()
 
-        low_idx = np.floor(timesteps).astype(int)
-        high_idx = np.ceil(timesteps).astype(int)
-        frac = np.mod(timesteps, 1.0)
+        schedule = np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps, dtype=float)
         sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
-        sigmas = (1 - frac) * sigmas[low_idx] + frac * sigmas[high_idx]
+        sigmas = np.interp(schedule[::-1], np.arange(0, len(sigmas)), sigmas)
         sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)
         self.sigmas = torch.from_numpy(sigmas)
+        self.schedule = torch.from_numpy(schedule)
 
-        self.timesteps = timesteps.astype(int)
         self.derivatives = []
 
     def step(
@@ -176,6 +197,8 @@ def step(
             When returning a tuple, the first element is the sample tensor.
 
         """
+        # FIXME: accounting for the descending sigmas
+        timestep = int(len(self.timesteps) - timestep - 1)
         sigma = self.sigmas[timestep]
 
         # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
@@ -209,12 +232,14 @@ def add_noise(
     ) -> torch.FloatTensor:
         sigmas = self.sigmas.to(original_samples.device)
         timesteps = timesteps.to(original_samples.device)
+        # FIXME: accounting for the descending sigmas
+        timesteps = self.num_inference_steps - timesteps - 1
 
-        sigma = sigmas[timesteps].flatten()
-        while len(sigma.shape) < len(original_samples.shape):
-            sigma = sigma.unsqueeze(-1)
+        sigmas = sigmas[timesteps].flatten()
+        while len(sigmas.shape) < len(original_samples.shape):
+            sigmas = sigmas.unsqueeze(-1)
 
-        noisy_samples = original_samples + noise * sigma
+        noisy_samples = original_samples + noise * sigmas
         return noisy_samples
 
     def __len__(self):
diff --git a/src/diffusers/schedulers/scheduling_pndm.py b/src/diffusers/schedulers/scheduling_pndm.py
index d9e430c4a656..6c4e307f5f31 100644
--- a/src/diffusers/schedulers/scheduling_pndm.py
+++ b/src/diffusers/schedulers/scheduling_pndm.py
@@ -22,7 +22,7 @@
 import torch
 
 from ..configuration_utils import ConfigMixin, register_to_config
-from .scheduling_utils import SchedulerMixin, SchedulerOutput
+from .scheduling_utils import BaseScheduler, SchedulerOutput
 
 
 def betas_for_alpha_bar(num_diffusion_timesteps, max_beta=0.999):
@@ -54,7 +54,7 @@ def alpha_bar(time_step):
     return torch.tensor(betas, dtype=torch.float32)
 
 
-class PNDMScheduler(SchedulerMixin, ConfigMixin):
+class PNDMScheduler(BaseScheduler, ConfigMixin):
     """
     Pseudo numerical methods for diffusion models (PNDM) proposes using more advanced ODE integration techniques,
     namely Runge-Kutta method and a linear multi-step method.
@@ -145,7 +145,13 @@ def __init__(
         self._timesteps = np.arange(0, num_train_timesteps)[::-1].copy()
         self.prk_timesteps = None
         self.plms_timesteps = None
-        self.timesteps = None
+        self.schedule = None
+
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for a model.
+        """
+        return self.schedule[step]
 
     def set_timesteps(self, num_inference_steps: int, **kwargs) -> torch.FloatTensor:
         """
@@ -190,7 +196,9 @@ def set_timesteps(self, num_inference_steps: int, **kwargs) -> torch.FloatTensor
                 ::-1
             ].copy()  # we copy to avoid having negative strides which are not supported by torch.from_numpy
 
-        self.timesteps = np.concatenate([self.prk_timesteps, self.plms_timesteps]).astype(np.int64)
+        self.schedule = np.concatenate([self.prk_timesteps, self.plms_timesteps]).astype(np.int64)
+        self.schedule = self.schedule[::-1].copy()  # FIXME: create the schedule in ascending order to avoid this
+        self.timesteps = np.arange(0, len(self.schedule))[::-1].copy()
 
         self.ets = []
         self.counter = 0
@@ -221,6 +229,7 @@ def step(
             returning a tuple, the first element is the sample tensor.
 
         """
+        timestep = self.schedule[timestep]
         if self.counter < len(self.prk_timesteps) and not self.config.skip_prk_steps:
             return self.step_prk(model_output=model_output, timestep=timestep, sample=sample, return_dict=return_dict)
         else:
@@ -395,6 +404,7 @@ def add_noise(
         if timesteps.device != original_samples.device:
             timesteps = timesteps.to(original_samples.device)
 
+        timesteps = self.schedule[timesteps]
         sqrt_alpha_prod = self.alphas_cumprod[timesteps] ** 0.5
         sqrt_alpha_prod = sqrt_alpha_prod.flatten()
         while len(sqrt_alpha_prod.shape) < len(original_samples.shape):
diff --git a/src/diffusers/schedulers/scheduling_sde_ve.py b/src/diffusers/schedulers/scheduling_sde_ve.py
index a549654c3b6f..6f2506195056 100644
--- a/src/diffusers/schedulers/scheduling_sde_ve.py
+++ b/src/diffusers/schedulers/scheduling_sde_ve.py
@@ -23,7 +23,7 @@
 
 from ..configuration_utils import ConfigMixin, register_to_config
 from ..utils import BaseOutput
-from .scheduling_utils import SchedulerMixin, SchedulerOutput
+from .scheduling_utils import BaseScheduler, SchedulerOutput
 
 
 @dataclass
@@ -43,7 +43,7 @@ class SdeVeOutput(BaseOutput):
     prev_sample_mean: torch.FloatTensor
 
 
-class ScoreSdeVeScheduler(SchedulerMixin, ConfigMixin):
+class ScoreSdeVeScheduler(BaseScheduler, ConfigMixin):
     """
     The variance exploding stochastic differential equation (SDE) scheduler.
 
@@ -90,6 +90,12 @@ def __init__(
 
         self.set_sigmas(num_train_timesteps, sigma_min, sigma_max, sampling_eps)
 
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for a model.
+        """
+        return self.timesteps[step]
+
     def set_timesteps(self, num_inference_steps: int, sampling_eps: float = None):
         """
         Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference.
diff --git a/src/diffusers/schedulers/scheduling_sde_vp.py b/src/diffusers/schedulers/scheduling_sde_vp.py
index daea743873f1..7cdeac19c50c 100644
--- a/src/diffusers/schedulers/scheduling_sde_vp.py
+++ b/src/diffusers/schedulers/scheduling_sde_vp.py
@@ -22,10 +22,10 @@
 import torch
 
 from ..configuration_utils import ConfigMixin, register_to_config
-from .scheduling_utils import SchedulerMixin
+from .scheduling_utils import BaseScheduler
 
 
-class ScoreSdeVpScheduler(SchedulerMixin, ConfigMixin):
+class ScoreSdeVpScheduler(BaseScheduler, ConfigMixin):
     """
     The variance preserving stochastic differential equation (SDE) scheduler.
 
@@ -52,6 +52,12 @@ def __init__(self, num_train_timesteps=2000, beta_min=0.1, beta_max=20, sampling
         self.discrete_sigmas = None
         self.timesteps = None
 
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for a model.
+        """
+        return self.discrete_sigmas[step]
+
     def set_timesteps(self, num_inference_steps):
         self.timesteps = torch.linspace(1, self.config.sampling_eps, num_inference_steps)
 
diff --git a/src/diffusers/schedulers/scheduling_utils.py b/src/diffusers/schedulers/scheduling_utils.py
index 1cc1d94414a6..30ad19664e05 100644
--- a/src/diffusers/schedulers/scheduling_utils.py
+++ b/src/diffusers/schedulers/scheduling_utils.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import abc
 import warnings
 from dataclasses import dataclass
 
@@ -36,6 +37,38 @@ class SchedulerOutput(BaseOutput):
     prev_sample: torch.FloatTensor
 
 
+class BaseScheduler(abc.ABC):
+    config_name = SCHEDULER_CONFIG_NAME
+
+    def scale_initial_noise(self, noise: torch.FloatTensor):
+        """
+        Scales the initial noise to the correct range for the scheduler.
+        """
+        return noise
+
+    def scale_model_input(self, sample: torch.FloatTensor, step: int):
+        """
+        Scales the model input (`sample`) to the correct range for the scheduler.
+        """
+        return sample
+
+    @abc.abstractmethod
+    def get_noise_condition(self, step: int):
+        """
+        Returns the input noise condition for the model (e.g. `timestep` or `sigma`).
+        """
+        raise NotImplementedError("Scheduler must implement the `get_noise_condition` function.")
+
+    def set_format(self, tensor_format="pt"):
+        warnings.warn(
+            "The method `set_format` is deprecated and will be removed in version `0.5.0`."
+            "If you're running your code in PyTorch, you can safely remove this function as the schedulers"
+            "are always in Pytorch",
+            DeprecationWarning,
+        )
+        return self
+
+
 class SchedulerMixin:
     """
     Mixin containing common functions for the schedulers.
diff --git a/tests/test_scheduler.py b/tests/test_scheduler.py
index cf3e607ea9d2..483d8bb6803f 100755
--- a/tests/test_scheduler.py
+++ b/tests/test_scheduler.py
@@ -201,7 +201,7 @@ def recursive_check(tuple_object, dict_object):
                 )
 
         kwargs = dict(self.forward_default_kwargs)
-        num_inference_steps = kwargs.pop("num_inference_steps", None)
+        num_inference_steps = kwargs.pop("num_inference_steps", 50)
 
         for scheduler_class in self.scheduler_classes:
             scheduler_config = self.get_scheduler_config()
@@ -336,9 +336,10 @@ def full_loop(self, **config):
 
         scheduler.set_timesteps(num_inference_steps)
 
-        for t in scheduler.timesteps:
+        for step in scheduler.timesteps:
+            t = scheduler.get_noise_condition(step)
             residual = model(sample, t)
-            sample = scheduler.step(residual, t, sample, eta).prev_sample
+            sample = scheduler.step(residual, step, sample, eta).prev_sample
 
         return sample
 
@@ -354,7 +355,7 @@ def test_steps_offset(self):
         scheduler_config = self.get_scheduler_config(steps_offset=1)
         scheduler = scheduler_class(**scheduler_config)
         scheduler.set_timesteps(5)
-        assert np.equal(scheduler.timesteps, np.array([801, 601, 401, 201, 1])).all()
+        assert np.equal(scheduler.schedule[scheduler.timesteps], np.array([801, 601, 401, 201, 1])).all()
 
     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]):
@@ -569,7 +570,7 @@ def test_steps_offset(self):
         scheduler = scheduler_class(**scheduler_config)
         scheduler.set_timesteps(10)
         assert np.equal(
-            scheduler.timesteps,
+            scheduler.schedule[scheduler.timesteps],
             np.array([901, 851, 851, 801, 801, 751, 751, 701, 701, 651, 651, 601, 601, 501, 401, 301, 201, 101, 1]),
         ).all()
 
@@ -863,18 +864,18 @@ def test_full_loop_no_noise(self):
         scheduler.set_timesteps(self.num_inference_steps)
 
         model = self.dummy_model()
-        sample = self.dummy_sample_deter * scheduler.sigmas[0]
-
-        for i, t in enumerate(scheduler.timesteps):
-            sample = sample / ((scheduler.sigmas[i] ** 2 + 1) ** 0.5)
+        sample = scheduler.scale_initial_noise(self.dummy_sample_deter)
 
+        for step in scheduler.timesteps:
+            sample = scheduler.scale_model_input(sample, step)
+            t = scheduler.get_noise_condition(step)
             model_output = model(sample, t)
 
-            output = scheduler.step(model_output, i, sample)
+            output = scheduler.step(model_output, step, sample)
             sample = output.prev_sample
 
         result_sum = torch.sum(torch.abs(sample))
         result_mean = torch.mean(torch.abs(sample))
 
-        assert abs(result_sum.item() - 1006.370) < 1e-2
+        assert abs(result_sum.item() - 1006.388) < 1e-2
         assert abs(result_mean.item() - 1.31) < 1e-3