Fast ODE-based Sampling for Diffusion Models in Around 5 Steps #8

diff --git a/docs/source/en/api/schedulers/amed.md b/docs/source/en/api/schedulers/amed.md
new file mode 100644
index 0000000..8ff69d7
--- /dev/null
+++ b/docs/source/en/api/schedulers/amed.md
@@ -0,0 +1,23 @@
+<!--Copyright 2025 The HuggingFace Team. All rights reserved.
+
+Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with
+the License. You may obtain a copy of the License at
+
+http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on
+an "AS IS" BASIS, 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.
+-->
+
+# AMEDScheduler
+
+The Approximate Mean-Direction (AMED) solver is from [Fast ODE-based Sampling for Diffusion Models in Around 5 Steps](https://huggingface.co/papers/2312.00094) by Zhenyu Zhou, Defang Chen, Can Wang, and Chun Chen. Each sampling step takes a single Euler hop to the geometric-mean intermediate noise level, evaluates the model there, and applies that mean-direction estimate across the whole step. This cancels the leading truncation error of an Euler step and produces high-quality samples in around five steps.
+
+This implementation is the training-free instantiation of the solver: the output-scaling coefficient `c` from the paper's plugin network defaults to `1.0` and is exposed through the `scale_factor` config argument for users who distill their own value. It reuses the noise-schedule construction and helpers of [`HeunDiscreteScheduler`] and can be selected for any Karras-style pipeline with `AMEDScheduler.from_config(pipe.scheduler.config)`.
+
+## AMEDScheduler
+[[autodoc]] AMEDScheduler
+
+## AMEDSchedulerOutput
+[[autodoc]] schedulers.scheduling_amed.AMEDSchedulerOutput
diff --git a/src/diffusers/__init__.py b/src/diffusers/__init__.py
index da77fa6..1c7918a 100644
--- a/src/diffusers/__init__.py
+++ b/src/diffusers/__init__.py
@@ -382,6 +382,7 @@ else:
     _import_structure["quantizers"] = ["DiffusersQuantizer"]
     _import_structure["schedulers"].extend(
         [
+            "AMEDScheduler",
             "AmusedScheduler",
             "BlockRefinementScheduler",
             "BlockRefinementSchedulerOutput",
@@ -1237,6 +1238,7 @@ if TYPE_CHECKING or DIFFUSERS_SLOW_IMPORT:
         )
         from .quantizers import DiffusersQuantizer
         from .schedulers import (
+            AMEDScheduler,
             AmusedScheduler,
             BlockRefinementScheduler,
             BlockRefinementSchedulerOutput,
diff --git a/src/diffusers/schedulers/__init__.py b/src/diffusers/schedulers/__init__.py
index 447586c..fecf726 100644
--- a/src/diffusers/schedulers/__init__.py
+++ b/src/diffusers/schedulers/__init__.py
@@ -39,6 +39,7 @@ except OptionalDependencyNotAvailable:
 
 else:
     _import_structure["deprecated"] = ["KarrasVeScheduler", "ScoreSdeVpScheduler"]
+    _import_structure["scheduling_amed"] = ["AMEDScheduler"]
     _import_structure["scheduling_amused"] = ["AmusedScheduler"]
     _import_structure["scheduling_block_refinement"] = ["BlockRefinementScheduler", "BlockRefinementSchedulerOutput"]
     _import_structure["scheduling_consistency_decoder"] = ["ConsistencyDecoderScheduler"]
@@ -146,6 +147,7 @@ if TYPE_CHECKING or DIFFUSERS_SLOW_IMPORT:
         from ..utils.dummy_pt_objects import *  # noqa F403
     else:
         from .deprecated import KarrasVeScheduler, ScoreSdeVpScheduler
+        from .scheduling_amed import AMEDScheduler
         from .scheduling_amused import AmusedScheduler
         from .scheduling_block_refinement import BlockRefinementScheduler, BlockRefinementSchedulerOutput
         from .scheduling_consistency_decoder import ConsistencyDecoderScheduler
diff --git a/src/diffusers/schedulers/scheduling_amed.py b/src/diffusers/schedulers/scheduling_amed.py
new file mode 100644
index 0000000..4eba31c
--- /dev/null
+++ b/src/diffusers/schedulers/scheduling_amed.py
@@ -0,0 +1,288 @@
+# Copyright 2025 The HuggingFace Team. All rights reserved.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# 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.
+
+# Adapted from "Fast ODE-based Sampling for Diffusion Models in Around 5 Steps"
+# (Zhou et al., https://huggingface.co/papers/2312.00094). The Approximate
+# Mean-Direction (AMED) solver replaces the endpoint-averaging of a second-order
+# Heun step with a single model evaluation at an intermediate noise level chosen
+# to approximate the mean ODE direction over the step. The paper learns the
+# intermediate position and an output-scaling coefficient with a tiny plugin
+# network; this scheduler implements the training-free instantiation, where the
+# intermediate noise level is the geometric mean of the step endpoints and the
+# scaling coefficient defaults to 1.0 (and is exposed via ``scale_factor`` for
+# users who distill their own value).
+
+from dataclasses import dataclass
+
+import numpy as np
+import torch
+
+from ..configuration_utils import register_to_config
+from ..utils import BaseOutput
+from .scheduling_heun_discrete import HeunDiscreteScheduler, betas_for_alpha_bar
+
+
+@dataclass
+class AMEDSchedulerOutput(BaseOutput):
+    """
+    Output class for the scheduler's `step` function output.
+
+    Args:
+        prev_sample (`torch.Tensor` of shape `(batch_size, num_channels, height, width)` for images):
+            Computed sample `(x_{t-1})` of previous timestep. `prev_sample` should be used as next mod