Error Propagation Mechanisms and Compensation Strategies for Quantized Diffusion Models

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.

Diffusion models can generate high-quality images, but they are costly to deploy because they refine images through many repeated denoising steps. Post-training quantization can speed up this process by using lower-precision computation, yet the small errors it introduces at each step can accumulate over the generation process and reduce image quality. This work analyzes how these quantization errors propagate in diffusion models and derives a closed-form description of the accumulated error. Based on this analysis, we propose a timestep-aware compensation method that corrects accumulated errors during sampling. Experiments on multiple image datasets show that the method improves existing quantization approaches with minimal extra cost, achieving a 1.2 PSNR gain over SVDQuant on SDXL W4A4 while adding less than 0.5% time overhead.