Temporal Quantization for Diffusion Models with Certified Error Bounds

Diffusion models generate high-quality samples, but repeated evaluations of large denoisers make deployment computationally expensive. Post-training quantization (PTQ) can reduce this cost, but how to verify and control quantization error through temporal quantization schemes remains challenging. To address this, we study temporal quantization of diffusion models, allowing deterministic, stochastic, and mixed-precision PTQ schemes across timesteps. By leveraging the $L_2$ moment generating function ($L_2$-MGF), we develop the first closed-form, high-probability error bound for diffusion process under arbitrary quantization schedules. Based on this theoretical guarantee, we build a predictive quantization policy which selects timestep-wise quantization schemes to minimize the terminal error bound under a computational budget. Extensive experiments evaluate both the error bounds and the resulting policies. More than 98.8% of the generated samples are within the 95%-certified quantization error bound. Across selected benchmarks, our proposed method reduces terminal \(L_2\) error by 23.1%, and LPIPS by 23.4% on average. On an NVIDIA RTX 5070Ti GPU, our method achieves at least 16.6% less GPU memory footprint and 12.9% less denoising time than the FP16 baseline.