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Diffusion models have been leveraged to perform adversarial purification andthus provide both empirical and certified robustness for a standard model. Onthe other hand, different robustly trained smoothed models have been studied toimprove the certified robustness. Thus, it raises a natural question: Candiffusion model be used to achieve improved certified robustness on thoserobustly trained smoothed models? In this work, we first theoretically showthat recovered instances by diffusion models are in the bounded neighborhood ofthe original instance with high probability; and the "one-shot" denoisingdiffusion probabilistic models (DDPM) can approximate the mean of the generateddistribution of a continuous-time diffusion model, which approximates theoriginal instance under mild conditions. Inspired by our analysis, we propose acertifiably robust pipeline DiffSmooth, which first performs adversarialpurification via diffusion models and then maps the purified instances to acommon region via a simple yet effective local smoothing strategy. We conductextensive experiments on different datasets and show that DiffSmooth achievesSOTA-certified robustness compared with eight baselines. For instance,DiffSmooth improves the SOTA-certified accuracy from $36.0\%$ to $53.0\%$ under$\ell_2$ radius $1.5$ on ImageNet. The code is available at[https://github.com/javyduck/DiffSmooth].

DiffSmooth: Certifiably Robust Learning via Diffusion Models and Local Smoothing