diffusers-dmse

MSE-optimal diffusion model scheduler (DMSE) for the HuggingFace diffusers library.

Inherits DDPMScheduler and modifies the reverse process to omit stochastic resampling, yielding a deterministic path that converges to the conditional mean estimator (CME) — the MSE-optimal denoiser.

Paper

B. Fesl, B. Böck, F. Strasser, M. Baur, M. Joham, W. Utschick, "On the Asymptotic Mean Square Error Optimality of Diffusion Models," AISTATS 2025.

[arXiv] [OpenReview] [PMLR]

Installation

pip install diffusers-dmse

Usage

Denoising a noisy observation (primary use case)

Use init_step() to find the timestep matching the observed SNR, then run the reverse process from that point. This implements Eq. (12) of the paper.

from diffusers import UNet2DModel
from diffusers_dmse import DMSEScheduler
import torch

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

scheduler = DMSEScheduler.from_pretrained("google/ddpm-cat-256")
model = UNet2DModel.from_pretrained("google/ddpm-cat-256").to(device)

# set_timesteps must be called before init_step
scheduler.set_timesteps(1000)

# Find starting timestep matching the observed SNR (in dB)
t_init, idx = scheduler.init_step(snr=10.0, is_logarithmic=True)

x = noisy_observation  # your input tensor, shape (B, C, H, W)
for t in scheduler.timesteps[idx:]:
    with torch.no_grad():
        eps = model(x, t).sample
    x = scheduler.step(eps, t, x).prev_sample

Unconditional generation (deterministic DDPM)

Drop-in replacement for DDPMScheduler. Runs the full reverse chain without noise, equivalent to DDIM with eta=0 using the DDPM posterior mean.

from diffusers import UNet2DModel
from diffusers_dmse import DMSEScheduler
import torch

device = torch.device("cuda" if torch.cuda.is_available() else "cpu")

scheduler = DMSEScheduler.from_pretrained("google/ddpm-cat-256")
model = UNet2DModel.from_pretrained("google/ddpm-cat-256").to(device)
scheduler.set_timesteps(50)

x = torch.randn((1, 3, 256, 256), device=device)
for t in scheduler.timesteps:
    with torch.no_grad():
        eps = model(x, t).sample
    x = scheduler.step(eps, t, x).prev_sample

Key difference from DDPMScheduler

	DDPM	DMSE
Reverse step	x_{t-1} = µ_t(x_t) + σ_t·z, z~N(0,I)	x_{t-1} = µ_t(x_t)
Stochastic	Yes	No
Optimal for	Generation diversity	MSE / denoising
Starting point	t=T (pure noise)	SNR-matched t via init_step()

Related repositories

• Diffusion_MSE: Full source code for the AISTATS 2025 paper, including GMM, MNIST, and audio experiments.
• Diffusion_channel_est: Application of DMSE to MIMO channel estimation (IEEE Wireless Communications Letters, 2024). [Paper]

License

MIT License. See LICENSE.