One-Step Offline Distillation of Diffusion-based Models via Koopman Modeling

TL;DR

This paper introduces Koopman Distillation Model (KDM), a novel approach that uses Koopman theory to enable single-step, efficient diffusion model distillation while maintaining semantic quality.

Contribution

The paper presents a new offline distillation framework for diffusion models based on Koopman theory, enabling one-step generation with theoretical and empirical validation.

Findings

KDM achieves competitive performance on standard benchmarks.

Theoretical justification for Koopman representation of diffusion dynamics.

Proximity in Koopman space correlates with semantic similarity.

Abstract

Diffusion-based generative models have demonstrated exceptional performance, yet their iterative sampling procedures remain computationally expensive. A prominent strategy to mitigate this cost is distillation, with offline distillation offering particular advantages in terms of efficiency, modularity, and flexibility. In this work, we identify two key observations that motivate a principled distillation framework: (1) while diffusion models have been viewed through the lens of dynamical systems theory, powerful and underexplored tools can be further leveraged; and (2) diffusion models inherently impose structured, semantically coherent trajectories in latent space. Building on these observations, we introduce the Koopman Distillation Model (KDM), a novel offline distillation approach grounded in Koopman theory - a classical framework for representing nonlinear dynamics linearly in a transformed space. KDM encodes noisy inputs into an embedded space where a learned linear operator propagates them forward, followed by a decoder that reconstructs clean samples. This enables single-step generation while preserving semantic fidelity. We provide theoretical justification for our approach: (1) under mild assumptions, the learned diffusion dynamics admit a finite-dimensional Koopman representation; and (2) proximity in the Koopman latent space correlates with semantic similarity in the generated outputs, allowing for effective trajectory alignment. KDM achieves highly competitive performance across standard offline distillation benchmarks.