Error Propagation Mechanisms and Compensation Strategies for Quantized Diffusion

TL;DR

This paper develops a theoretical framework for understanding error propagation in quantized diffusion models and proposes a compensation strategy that improves image synthesis quality with minimal additional computation.

Contribution

It introduces the first closed-form solution for cumulative error in diffusion models and a timestep-aware compensation scheme to mitigate quantization errors.

Findings

Achieves 1.2 PSNR improvement over SVDQuant on SDXL W4A4.

Effectively mitigates error propagation in quantized diffusion models.

Adds less than 0.5% time overhead to existing methods.

Abstract

Diffusion models have transformed image synthesis by establishing unprecedented quality and creativity benchmarks. Nevertheless, their large-scale deployment faces challenges due to computationally intensive iterative denoising processes. Although post-training quantization (PTQ) provides an effective pathway for accelerating sampling, the iterative nature of diffusion models causes stepwise quantization errors to accumulate progressively during generation, inevitably compromising output fidelity. To address this challenge, we develop a theoretical framework that mathematically formulates error propagation in Diffusion Models (DMs), deriving per-step quantization error propagation equations and establishing the first closed-form solution for cumulative error. Building on this theoretical foundation, we propose a timestep-aware cumulative error compensation scheme. Extensive experiments on multiple image datasets demonstrate that our compensation strategy effectively mitigates error propagation, significantly enhancing existing PTQ methods. Specifically, it achieves a 1.2 PSNR improvement over SVDQuant on SDXL W4A4, while incurring only an additional $<$ 0.5\% time overhead.