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Restoration Score Distillation: From Corrupted Diffusion Pretraining to One-Step High-Quality Generation

Yasi Zhang, Tianyu Chen, Zhendong Wang, Ying Nian Wu, Mingyuan Zhou, Oscar Leong

TL;DR

Restoration Score Distillation (RSD) extends denoising score distillation to a broad class of corruptions by first pretraining a diffusion teacher on corrupted data and then distilling it into a fast one-step generator. The approach unifies and enhances corruption-aware diffusion techniques (Ambient Tweedie, Ambient Diffusion, Fourier-space Ambient Diffusion) and is supported by a theoretical result showing eigenspace alignment in linear settings, providing a principled regularization mechanism. Empirically, RSD improves generation quality on natural images and medical MRI, often surpassing the teacher and competing baselines, while offering substantial data and runtime efficiency. The work demonstrates that degraded data, when leveraged via score distillation, can yield superior supervision for robust generative modeling in domains where clean data are scarce or expensive. These findings suggest broad applicability to scientific imaging and other corrupted-data scenarios, with potential extensions to conditional sampling and inverse problems.

Abstract

Learning generative models from corrupted data is a fundamental yet persistently challenging task across scientific disciplines, particularly when access to clean data is limited or expensive. Denoising Score Distillation (DSD) \cite{chen2025denoising} recently introduced a novel and surprisingly effective strategy that leverages score distillation to train high-fidelity generative models directly from noisy observations. Building upon this foundation, we propose \textit{Restoration Score Distillation} (RSD), a principled generalization of DSD that accommodates a broader range of corruption types, such as blurred, incomplete, or low-resolution images. RSD operates by first pretraining a teacher diffusion model solely on corrupted data and subsequently distilling it into a single-step generator that produces high-quality reconstructions. Empirically, RSD consistently surpasses its teacher model across diverse restoration tasks on both natural and scientific datasets. Moreover, beyond standard diffusion objectives, the RSD framework is compatible with several corruption-aware training techniques such as Ambient Tweedie, Ambient Diffusion, and its Fourier-space variant, enabling flexible integration with recent advances in diffusion modeling. Theoretically, we demonstrate that in a linear regime, RSD recovers the eigenspace of the clean data covariance matrix from linear measurements, thereby serving as an implicit regularizer. This interpretation recasts score distillation not only as a sampling acceleration technique but as a principled approach to enhancing generative performance in severely degraded data regimes.

Restoration Score Distillation: From Corrupted Diffusion Pretraining to One-Step High-Quality Generation

TL;DR

Restoration Score Distillation (RSD) extends denoising score distillation to a broad class of corruptions by first pretraining a diffusion teacher on corrupted data and then distilling it into a fast one-step generator. The approach unifies and enhances corruption-aware diffusion techniques (Ambient Tweedie, Ambient Diffusion, Fourier-space Ambient Diffusion) and is supported by a theoretical result showing eigenspace alignment in linear settings, providing a principled regularization mechanism. Empirically, RSD improves generation quality on natural images and medical MRI, often surpassing the teacher and competing baselines, while offering substantial data and runtime efficiency. The work demonstrates that degraded data, when leveraged via score distillation, can yield superior supervision for robust generative modeling in domains where clean data are scarce or expensive. These findings suggest broad applicability to scientific imaging and other corrupted-data scenarios, with potential extensions to conditional sampling and inverse problems.

Abstract

Learning generative models from corrupted data is a fundamental yet persistently challenging task across scientific disciplines, particularly when access to clean data is limited or expensive. Denoising Score Distillation (DSD) \cite{chen2025denoising} recently introduced a novel and surprisingly effective strategy that leverages score distillation to train high-fidelity generative models directly from noisy observations. Building upon this foundation, we propose \textit{Restoration Score Distillation} (RSD), a principled generalization of DSD that accommodates a broader range of corruption types, such as blurred, incomplete, or low-resolution images. RSD operates by first pretraining a teacher diffusion model solely on corrupted data and subsequently distilling it into a single-step generator that produces high-quality reconstructions. Empirically, RSD consistently surpasses its teacher model across diverse restoration tasks on both natural and scientific datasets. Moreover, beyond standard diffusion objectives, the RSD framework is compatible with several corruption-aware training techniques such as Ambient Tweedie, Ambient Diffusion, and its Fourier-space variant, enabling flexible integration with recent advances in diffusion modeling. Theoretically, we demonstrate that in a linear regime, RSD recovers the eigenspace of the clean data covariance matrix from linear measurements, thereby serving as an implicit regularizer. This interpretation recasts score distillation not only as a sampling acceleration technique but as a principled approach to enhancing generative performance in severely degraded data regimes.
Paper Structure (46 sections, 3 theorems, 49 equations, 28 figures, 6 tables, 6 algorithms)

This paper contains 46 sections, 3 theorems, 49 equations, 28 figures, 6 tables, 6 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Diffusion Models
  4. Diffusion Models for Corruptions
  5. Ambient Tweedie for Noisy Corruptions.
  6. Ambient Diffusion for Masked Observations.
  7. Fourier-Space Ambient Diffusion for Frequency-Domain Corruptions.
  8. Score Distillation for Generative Modeling
  9. Restoration Score Distillation
  10. Problem Statement.
  11. Phase I: Flexible Corruption-Aware Pretraining
  12. Phase II: One-Step Generator Distillation
  13. Theoretical Analysis
  14. Experiments
  15. Natural Images
  16. ...and 31 more sections

Key Result

Theorem 1

Fix $\sigma > 0$ and consider $e \in \mathbb{R}^d$ with unit norm and $Ae\neq0$. Under Assumptions assump:linear, aasump:perfect_score, and assump:low_rank_generator and any bounded noise schedule $(\sigma_t) \subseteq [\sigma_{\min},\sigma_{\max}]$, the set of global minimizers of the loss eq:ideal If $e \in \mathrm{Im}(A^T)$, we have that $\theta_*=\theta_*(u_*)$ with the minimum norm solution $

Figures (28)

  • Figure 1: Illustration of our RSD framework and its results across diverse restoration tasks, including Gaussian deblurring, random inpainting, and super-resolution. Additional qualitative examples are provided in Appendix \ref{['app:snapshot']}.
  • Figure 1: Summary of corruption-aware diffusion objectives used for pretraining. Our framework can be seamlessly integrated with existing advanced corruption-aware diffusion objectives.
  • Figure 2: RSD vs Teacher Models
  • Figure 3: Qualitative results of our method RSD on multi-coil MRI.
  • Figure 4: Proximal FID for model selection in the Super-Resolution task with $\sigma=0$.
  • ...and 23 more figures

Theorems & Definitions (5)

  • Theorem 1
  • Lemma 1
  • Lemma 2
  • proof : Proof of Lemma \ref{['lem:objective-reduction']}
  • proof : Proof of Theorem \ref{['thm:global-min-thm']}