diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
index ce17f2e0ee41..9f1211b43013 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
@@ -6,6 +6,7 @@
 
 from transformers import CLIPFeatureExtractor, CLIPTextModel, CLIPTokenizer
 
+from ...configuration_utils import FrozenDict
 from ...models import AutoencoderKL, UNet2DConditionModel
 from ...pipeline_utils import DiffusionPipeline
 from ...schedulers import DDIMScheduler, LMSDiscreteScheduler, PNDMScheduler
@@ -53,6 +54,21 @@ def __init__(
     ):
         super().__init__()
         scheduler = scheduler.set_format("pt")
+
+        if hasattr(scheduler.config, "steps_offset") and scheduler.config.steps_offset != 1:
+            warnings.warn(
+                f"The configuration file of this scheduler: {scheduler} is outdated. `steps_offset`"
+                f" should be set to 1 istead of {scheduler.config.steps_offset}. Please make sure "
+                "to update the config accordingly as leaving `steps_offset` might led to incorrect results"
+                " in future versions. If you have downloaded this checkpoint from the Hugging Face Hub,"
+                " it would be very nice if you could open a Pull request for the `scheduler/scheduler_config.json`"
+                " file",
+                DeprecationWarning,
+            )
+            new_config = dict(scheduler.config)
+            new_config["steps_offset"] = 1
+            scheduler._internal_dict = FrozenDict(new_config)
+
         self.register_modules(
             vae=vae,
             text_encoder=text_encoder,
@@ -217,12 +233,7 @@ def __call__(
         latents = latents.to(self.device)
 
         # set timesteps
-        accepts_offset = "offset" in set(inspect.signature(self.scheduler.set_timesteps).parameters.keys())
-        extra_set_kwargs = {}
-        if accepts_offset:
-            extra_set_kwargs["offset"] = 1
-
-        self.scheduler.set_timesteps(num_inference_steps, **extra_set_kwargs)
+        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):
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 817288f499ec..e7adb4d1a33b 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
@@ -1,4 +1,5 @@
 import inspect
+import warnings
 from typing import List, Optional, Union
 
 import numpy as np
@@ -7,6 +8,7 @@
 import PIL
 from transformers import CLIPFeatureExtractor, CLIPTextModel, CLIPTokenizer
 
+from ...configuration_utils import FrozenDict
 from ...models import AutoencoderKL, UNet2DConditionModel
 from ...pipeline_utils import DiffusionPipeline
 from ...schedulers import DDIMScheduler, LMSDiscreteScheduler, PNDMScheduler
@@ -64,6 +66,21 @@ def __init__(
     ):
         super().__init__()
         scheduler = scheduler.set_format("pt")
+
+        if hasattr(scheduler.config, "steps_offset") and scheduler.config.steps_offset != 1:
+            warnings.warn(
+                f"The configuration file of this scheduler: {scheduler} is outdated. `steps_offset`"
+                f" should be set to 1 istead of {scheduler.config.steps_offset}. Please make sure "
+                "to update the config accordingly as leaving `steps_offset` might led to incorrect results"
+                " in future versions. If you have downloaded this checkpoint from the Hugging Face Hub,"
+                " it would be very nice if you could open a Pull request for the `scheduler/scheduler_config.json`"
+                " file",
+                DeprecationWarning,
+            )
+            new_config = dict(scheduler.config)
+            new_config["steps_offset"] = 1
+            scheduler._internal_dict = FrozenDict(new_config)
+
         self.register_modules(
             vae=vae,
             text_encoder=text_encoder,
@@ -169,14 +186,7 @@ def __call__(
             raise ValueError(f"The value of strength should in [0.0, 1.0] but is {strength}")
 
         # set timesteps
-        accepts_offset = "offset" in set(inspect.signature(self.scheduler.set_timesteps).parameters.keys())
-        extra_set_kwargs = {}
-        offset = 0
-        if accepts_offset:
-            offset = 1
-            extra_set_kwargs["offset"] = 1
-
-        self.scheduler.set_timesteps(num_inference_steps, **extra_set_kwargs)
+        self.scheduler.set_timesteps(num_inference_steps)
 
         if isinstance(init_image, PIL.Image.Image):
             init_image = preprocess(init_image)
@@ -190,6 +200,7 @@ def __call__(
         init_latents = torch.cat([init_latents] * batch_size)
 
         # get the original timestep using init_timestep
+        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):
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 6076b854089e..b9ad36f1a2bf 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
@@ -1,4 +1,5 @@
 import inspect
+import warnings
 from typing import List, Optional, Union
 
 import numpy as np
@@ -8,6 +9,7 @@
 from tqdm.auto import tqdm
 from transformers import CLIPFeatureExtractor, CLIPTextModel, CLIPTokenizer
 
+from ...configuration_utils import FrozenDict
 from ...models import AutoencoderKL, UNet2DConditionModel
 from ...pipeline_utils import DiffusionPipeline
 from ...schedulers import DDIMScheduler, PNDMScheduler
@@ -83,6 +85,21 @@ def __init__(
         super().__init__()
         scheduler = scheduler.set_format("pt")
         logger.info("`StableDiffusionInpaintPipeline` is experimental and will very likely change in the future.")
+
+        if hasattr(scheduler.config, "steps_offset") and scheduler.config.steps_offset != 1:
+            warnings.warn(
+                f"The configuration file of this scheduler: {scheduler} is outdated. `steps_offset`"
+                f" should be set to 1 istead of {scheduler.config.steps_offset}. Please make sure "
+                "to update the config accordingly as leaving `steps_offset` might led to incorrect results"
+                " in future versions. If you have downloaded this checkpoint from the Hugging Face Hub,"
+                " it would be very nice if you could open a Pull request for the `scheduler/scheduler_config.json`"
+                " file",
+                DeprecationWarning,
+            )
+            new_config = dict(scheduler.config)
+            new_config["steps_offset"] = 1
+            scheduler._internal_dict = FrozenDict(new_config)
+
         self.register_modules(
             vae=vae,
             text_encoder=text_encoder,
@@ -193,19 +210,12 @@ def __call__(
             raise ValueError(f"The value of strength should in [0.0, 1.0] but is {strength}")
 
         # set timesteps
-        accepts_offset = "offset" in set(inspect.signature(self.scheduler.set_timesteps).parameters.keys())
-        extra_set_kwargs = {}
-        offset = 0
-        if accepts_offset:
-            offset = 1
-            extra_set_kwargs["offset"] = 1
-
-        self.scheduler.set_timesteps(num_inference_steps, **extra_set_kwargs)
+        self.scheduler.set_timesteps(num_inference_steps)
 
         # preprocess image
         if not isinstance(init_image, torch.FloatTensor):
             init_image = preprocess_image(init_image)
-        init_image.to(self.device)
+        init_image = init_image.to(self.device)
 
         # encode the init image into latents and scale the latents
         init_latent_dist = self.vae.encode(init_image).latent_dist
@@ -220,7 +230,7 @@ def __call__(
         # preprocess mask
         if not isinstance(mask_image, torch.FloatTensor):
             mask_image = preprocess_mask(mask_image)
-        mask_image.to(self.device)
+        mask_image = mask_image.to(self.device)
         mask = torch.cat([mask_image] * batch_size)
 
         # check sizes
@@ -228,6 +238,7 @@ def __call__(
             raise ValueError("The mask and init_image should be the same size!")
 
         # get the original timestep using init_timestep
+        offset = self.scheduler.config.get("steps_offset", 0)
         init_timestep = int(num_inference_steps * strength) + offset
         init_timestep = min(init_timestep, num_inference_steps)
         timesteps = self.scheduler.timesteps[-init_timestep]
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 b114145d6f04..ccba29ade5d3 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
@@ -100,12 +100,7 @@ def __call__(
             raise ValueError(f"Unexpected latents shape, got {latents.shape}, expected {latents_shape}")
 
         # set timesteps
-        accepts_offset = "offset" in set(inspect.signature(self.scheduler.set_timesteps).parameters.keys())
-        extra_set_kwargs = {}
-        if accepts_offset:
-            extra_set_kwargs["offset"] = 1
-
-        self.scheduler.set_timesteps(num_inference_steps, **extra_set_kwargs)
+        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):
diff --git a/src/diffusers/schedulers/scheduling_ddim.py b/src/diffusers/schedulers/scheduling_ddim.py
index 85ba67523172..32be871f0bc9 100644
--- a/src/diffusers/schedulers/scheduling_ddim.py
+++ b/src/diffusers/schedulers/scheduling_ddim.py
@@ -16,6 +16,7 @@
 # and https://github.com/hojonathanho/diffusion
 
 import math
+import warnings
 from typing import Optional, Tuple, Union
 
 import numpy as np
@@ -78,7 +79,13 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         clip_sample (`bool`, default `True`):
             option to clip predicted sample between -1 and 1 for numerical stability.
         set_alpha_to_one (`bool`, default `True`):
-            if alpha for final step is 1 or the final alpha of the "non-previous" one.
+            each diffusion step uses the value of alphas product at that step and at the previous one. For the final
+            step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
+            otherwise it uses the value of alpha at step 0.
+        steps_offset (`int`, default `0`):
+            an offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
+            stable diffusion.
         tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays.
 
     """
@@ -93,6 +100,7 @@ def __init__(
         trained_betas: Optional[np.ndarray] = None,
         clip_sample: bool = True,
         set_alpha_to_one: bool = True,
+        steps_offset: int = 0,
         tensor_format: str = "pt",
     ):
         if trained_betas is not None:
@@ -134,16 +142,26 @@ def _get_variance(self, timestep, prev_timestep):
 
         return variance
 
-    def set_timesteps(self, num_inference_steps: int, offset: int = 0):
+    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.
 
         Args:
             num_inference_steps (`int`):
                 the number of diffusion steps used when generating samples with a pre-trained model.
-            offset (`int`):
-                optional value to shift timestep values up by. A value of 1 is used in stable diffusion for inference.
         """
+
+        offset = self.config.steps_offset
+
+        if "offset" in kwargs:
+            warnings.warn(
+                "`offset` is deprecated as an input argument to `set_timesteps` and will be removed in v0.4.0."
+                " Please pass `steps_offset` to `__init__` instead.",
+                DeprecationWarning,
+            )
+
+            offset = kwargs["offset"]
+
         self.num_inference_steps = num_inference_steps
         step_ratio = self.config.num_train_timesteps // self.num_inference_steps
         # creates integer timesteps by multiplying by ratio
diff --git a/src/diffusers/schedulers/scheduling_pndm.py b/src/diffusers/schedulers/scheduling_pndm.py
index 6eeb15b93923..09e8a7e240c2 100644
--- a/src/diffusers/schedulers/scheduling_pndm.py
+++ b/src/diffusers/schedulers/scheduling_pndm.py
@@ -15,6 +15,7 @@
 # DISCLAIMER: This file is strongly influenced by https://github.com/ermongroup/ddim
 
 import math
+import warnings
 from typing import Optional, Tuple, Union
 
 import numpy as np
@@ -74,10 +75,18 @@ class PNDMScheduler(SchedulerMixin, ConfigMixin):
             `linear`, `scaled_linear`, or `squaredcos_cap_v2`.
         trained_betas (`np.ndarray`, optional):
             option to pass an array of betas directly to the constructor to bypass `beta_start`, `beta_end` etc.
-        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays
         skip_prk_steps (`bool`):
             allows the scheduler to skip the Runge-Kutta steps that are defined in the original paper as being required
             before plms steps; defaults to `False`.
+        set_alpha_to_one (`bool`, default `False`):
+            each diffusion step uses the value of alphas product at that step and at the previous one. For the final
+            step there is no previous alpha. When this option is `True` the previous alpha product is fixed to `1`,
+            otherwise it uses the value of alpha at step 0.
+        steps_offset (`int`, default `0`):
+            an offset added to the inference steps. You can use a combination of `offset=1` and
+            `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
+            stable diffusion.
+        tensor_format (`str`): whether the scheduler expects pytorch or numpy arrays
 
     """
 
@@ -89,8 +98,10 @@ def __init__(
         beta_end: float = 0.02,
         beta_schedule: str = "linear",
         trained_betas: Optional[np.ndarray] = None,
-        tensor_format: str = "pt",
         skip_prk_steps: bool = False,
+        set_alpha_to_one: bool = False,
+        steps_offset: int = 0,
+        tensor_format: str = "pt",
     ):
         if trained_betas is not None:
             self.betas = np.asarray(trained_betas)
@@ -108,6 +119,8 @@ def __init__(
         self.alphas = 1.0 - self.betas
         self.alphas_cumprod = np.cumprod(self.alphas, axis=0)
 
+        self.final_alpha_cumprod = np.array(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
+
         # For now we only support F-PNDM, i.e. the runge-kutta method
         # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
         # mainly at formula (9), (12), (13) and the Algorithm 2.
@@ -122,7 +135,6 @@ def __init__(
         # setable values
         self.num_inference_steps = None
         self._timesteps = np.arange(0, num_train_timesteps)[::-1].copy()
-        self._offset = 0
         self.prk_timesteps = None
         self.plms_timesteps = None
         self.timesteps = None
@@ -130,23 +142,31 @@ def __init__(
         self.tensor_format = tensor_format
         self.set_format(tensor_format=tensor_format)
 
-    def set_timesteps(self, num_inference_steps: int, offset: int = 0) -> torch.FloatTensor:
+    def set_timesteps(self, num_inference_steps: int, **kwargs) -> torch.FloatTensor:
         """
         Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
 
         Args:
             num_inference_steps (`int`):
                 the number of diffusion steps used when generating samples with a pre-trained model.
-            offset (`int`):
-                optional value to shift timestep values up by. A value of 1 is used in stable diffusion for inference.
         """
+
+        offset = self.config.steps_offset
+
+        if "offset" in kwargs:
+            warnings.warn(
+                "`offset` is deprecated as an input argument to `set_timesteps` and will be removed in v0.4.0."
+                " Please pass `steps_offset` to `__init__` instead."
+            )
+
+            offset = kwargs["offset"]
+
         self.num_inference_steps = num_inference_steps
         step_ratio = self.config.num_train_timesteps // self.num_inference_steps
         # creates integer timesteps by multiplying by ratio
         # casting to int to avoid issues when num_inference_step is power of 3
-        self._timesteps = (np.arange(0, num_inference_steps) * step_ratio).round().tolist()
-        self._offset = offset
-        self._timesteps = np.array([t + self._offset for t in self._timesteps])
+        self._timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()
+        self._timesteps += offset
 
         if self.config.skip_prk_steps:
             # for some models like stable diffusion the prk steps can/should be skipped to
@@ -231,7 +251,7 @@ def step_prk(
             )
 
         diff_to_prev = 0 if self.counter % 2 else self.config.num_train_timesteps // self.num_inference_steps // 2
-        prev_timestep = max(timestep - diff_to_prev, self.prk_timesteps[-1])
+        prev_timestep = timestep - diff_to_prev
         timestep = self.prk_timesteps[self.counter // 4 * 4]
 
         if self.counter % 4 == 0:
@@ -293,7 +313,7 @@ def step_plms(
                 "for more information."
             )
 
-        prev_timestep = max(timestep - self.config.num_train_timesteps // self.num_inference_steps, 0)
+        prev_timestep = timestep - self.config.num_train_timesteps // self.num_inference_steps
 
         if self.counter != 1:
             self.ets.append(model_output)
@@ -323,7 +343,7 @@ def step_plms(
 
         return SchedulerOutput(prev_sample=prev_sample)
 
-    def _get_prev_sample(self, sample, timestep, timestep_prev, model_output):
+    def _get_prev_sample(self, sample, timestep, prev_timestep, model_output):
         # See formula (9) of PNDM paper https://arxiv.org/pdf/2202.09778.pdf
         # this function computes x_(t−δ) using the formula of (9)
         # Note that x_t needs to be added to both sides of the equation
@@ -336,8 +356,8 @@ def _get_prev_sample(self, sample, timestep, timestep_prev, model_output):
         # sample -> x_t
         # model_output -> e_θ(x_t, t)
         # prev_sample -> x_(t−δ)
-        alpha_prod_t = self.alphas_cumprod[timestep + 1 - self._offset]
-        alpha_prod_t_prev = self.alphas_cumprod[timestep_prev + 1 - self._offset]
+        alpha_prod_t = self.alphas_cumprod[timestep]
+        alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
         beta_prod_t = 1 - alpha_prod_t
         beta_prod_t_prev = 1 - alpha_prod_t_prev
 
diff --git a/tests/test_scheduler.py b/tests/test_scheduler.py
index e78f100409f8..7377797bebfa 100755
--- a/tests/test_scheduler.py
+++ b/tests/test_scheduler.py
@@ -357,10 +357,38 @@ def get_scheduler_config(self, **kwargs):
         config.update(**kwargs)
         return config
 
+    def full_loop(self, **config):
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(**config)
+        scheduler = scheduler_class(**scheduler_config)
+
+        num_inference_steps, eta = 10, 0.0
+
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter
+
+        scheduler.set_timesteps(num_inference_steps)
+
+        for t in scheduler.timesteps:
+            residual = model(sample, t)
+            sample = scheduler.step(residual, t, sample, eta).prev_sample
+
+        return sample
+
     def test_timesteps(self):
         for timesteps in [100, 500, 1000]:
             self.check_over_configs(num_train_timesteps=timesteps)
 
+    def test_steps_offset(self):
+        for steps_offset in [0, 1]:
+            self.check_over_configs(steps_offset=steps_offset)
+
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(steps_offset=1)
+        scheduler = scheduler_class(**scheduler_config)
+        scheduler.set_timesteps(5)
+        assert torch.equal(scheduler.timesteps, torch.tensor([801, 601, 401, 201, 1]))
+
     def test_betas(self):
         for beta_start, beta_end in zip([0.0001, 0.001, 0.01, 0.1], [0.002, 0.02, 0.2, 2]):
             self.check_over_configs(beta_start=beta_start, beta_end=beta_end)
@@ -398,26 +426,31 @@ def test_variance(self):
         assert torch.sum(torch.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)
+        sample = self.full_loop()
 
-        num_inference_steps, eta = 10, 0.0
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
 
-        model = self.dummy_model()
-        sample = self.dummy_sample_deter
+        assert abs(result_sum.item() - 172.0067) < 1e-2
+        assert abs(result_mean.item() - 0.223967) < 1e-3
 
-        scheduler.set_timesteps(num_inference_steps)
-        for t in scheduler.timesteps:
-            residual = model(sample, t)
+    def test_full_loop_with_set_alpha_to_one(self):
+        # We specify different beta, so that the first alpha is 0.99
+        sample = self.full_loop(set_alpha_to_one=True, beta_start=0.01)
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
 
-            sample = scheduler.step(residual, t, sample, eta).prev_sample
+        assert abs(result_sum.item() - 149.8295) < 1e-2
+        assert abs(result_mean.item() - 0.1951) < 1e-3
 
+    def test_full_loop_with_no_set_alpha_to_one(self):
+        # We specify different beta, so that the first alpha is 0.99
+        sample = self.full_loop(set_alpha_to_one=False, beta_start=0.01)
         result_sum = torch.sum(torch.abs(sample))
         result_mean = torch.mean(torch.abs(sample))
 
-        assert abs(result_sum.item() - 172.0067) < 1e-2
-        assert abs(result_mean.item() - 0.223967) < 1e-3
+        assert abs(result_sum.item() - 149.0784) < 1e-2
+        assert abs(result_mean.item() - 0.1941) < 1e-3
 
 
 class PNDMSchedulerTest(SchedulerCommonTest):
@@ -503,6 +536,26 @@ def check_over_forward(self, time_step=0, **forward_kwargs):
 
             assert torch.sum(torch.abs(output - new_output)) < 1e-5, "Scheduler outputs are not identical"
 
+    def full_loop(self, **config):
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(**config)
+        scheduler = scheduler_class(**scheduler_config)
+
+        num_inference_steps = 10
+        model = self.dummy_model()
+        sample = self.dummy_sample_deter
+        scheduler.set_timesteps(num_inference_steps)
+
+        for i, t in enumerate(scheduler.prk_timesteps):
+            residual = model(sample, t)
+            sample = scheduler.step_prk(residual, t, sample).prev_sample
+
+        for i, t in enumerate(scheduler.plms_timesteps):
+            residual = model(sample, t)
+            sample = scheduler.step_plms(residual, t, sample).prev_sample
+
+        return sample
+
     def test_pytorch_equal_numpy(self):
         kwargs = dict(self.forward_default_kwargs)
         num_inference_steps = kwargs.pop("num_inference_steps", None)
@@ -606,8 +659,23 @@ def test_timesteps(self):
         for timesteps in [100, 1000]:
             self.check_over_configs(num_train_timesteps=timesteps)
 
+    def test_steps_offset(self):
+        for steps_offset in [0, 1]:
+            self.check_over_configs(steps_offset=steps_offset)
+
+        scheduler_class = self.scheduler_classes[0]
+        scheduler_config = self.get_scheduler_config(steps_offset=1)
+        scheduler = scheduler_class(**scheduler_config)
+        scheduler.set_timesteps(10)
+        assert torch.equal(
+            scheduler.timesteps,
+            torch.tensor(
+                [901, 851, 851, 801, 801, 751, 751, 701, 701, 651, 651, 601, 601, 501, 401, 301, 201, 101, 1]
+            ),
+        )
+
     def test_betas(self):
-        for beta_start, beta_end in zip([0.0001, 0.001, 0.01], [0.002, 0.02, 0.2]):
+        for beta_start, beta_end in zip([0.0001, 0.001], [0.002, 0.02]):
             self.check_over_configs(beta_start=beta_start, beta_end=beta_end)
 
     def test_schedules(self):
@@ -620,7 +688,7 @@ def test_time_indices(self):
 
     def test_inference_steps(self):
         for t, num_inference_steps in zip([1, 5, 10], [10, 50, 100]):
-            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_pow_of_3_inference_steps(self):
         # earlier version of set_timesteps() caused an error indexing alpha's with inference steps as power of 3
@@ -648,28 +716,30 @@ def test_inference_plms_no_past_residuals(self):
             scheduler.step_plms(self.dummy_sample, 1, self.dummy_sample).prev_sample
 
     def test_full_loop_no_noise(self):
-        scheduler_class = self.scheduler_classes[0]
-        scheduler_config = self.get_scheduler_config()
-        scheduler = scheduler_class(**scheduler_config)
+        sample = self.full_loop()
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
 
-        num_inference_steps = 10
-        model = self.dummy_model()
-        sample = self.dummy_sample_deter
-        scheduler.set_timesteps(num_inference_steps)
+        assert abs(result_sum.item() - 198.1318) < 1e-2
+        assert abs(result_mean.item() - 0.2580) < 1e-3
 
-        for i, t in enumerate(scheduler.prk_timesteps):
-            residual = model(sample, t)
-            sample = scheduler.step_prk(residual, i, sample).prev_sample
+    def test_full_loop_with_set_alpha_to_one(self):
+        # We specify different beta, so that the first alpha is 0.99
+        sample = self.full_loop(set_alpha_to_one=True, beta_start=0.01)
+        result_sum = torch.sum(torch.abs(sample))
+        result_mean = torch.mean(torch.abs(sample))
 
-        for i, t in enumerate(scheduler.plms_timesteps):
-            residual = model(sample, t)
-            sample = scheduler.step_plms(residual, i, sample).prev_sample
+        assert abs(result_sum.item() - 230.0399) < 1e-2
+        assert abs(result_mean.item() - 0.2995) < 1e-3
 
+    def test_full_loop_with_no_set_alpha_to_one(self):
+        # We specify different beta, so that the first alpha is 0.99
+        sample = self.full_loop(set_alpha_to_one=False, beta_start=0.01)
         result_sum = torch.sum(torch.abs(sample))
         result_mean = torch.mean(torch.abs(sample))
 
-        assert abs(result_sum.item() - 428.8788) < 1e-2
-        assert abs(result_mean.item() - 0.5584) < 1e-3
+        assert abs(result_sum.item() - 186.9482) < 1e-2
+        assert abs(result_mean.item() - 0.2434) < 1e-3
 
 
 class ScoreSdeVeSchedulerTest(unittest.TestCase):