Risk-Sensitive Diffusion: Robustly Optimizing Diffusion Models with Noisy Samples

Diffusion models are mainly studied on image data. However, non-image data (e.g., tabular data) are also prevalent in real applications and tend to be noisy due to some inevitable factors in the stage of data collection, degrading the generation quality of diffusion models. In this paper, we consider a novel problem setting where every collected sample is paired with a vector indicating the data quality: risk vector. This setting applies to many scenarios involving noisy data and we propose risk-sensitive SDE, a type of stochastic differential equation (SDE) parameterized by the risk vector, to address it. With some proper coefficients, risk-sensitive SDE can minimize the negative effect of noisy samples on the optimization of diffusion models. We conduct systematic studies for both Gaussian and non-Gaussian noise distributions, providing analytical forms of risk-sensitive SDE. To verify the effectiveness of our method, we have conducted extensive experiments on multiple tabular and time-series datasets, showing that risk-sensitive SDE permits a robust optimization of diffusion models with noisy samples and significantly outperforms previous baselines. INTRODUCTION Prevalence of noisy non-image data. Current studies on diffusion models (Sohl-Dickstein et al., 2015; Ho et al., 2020) (or score-based generative models (Song & Ermon, 2019; Song et al., 2021) ) have primarily focused on high-quality image data, achieving promising performance (Dhariwal & Nichol, 2021) in image synthesis. However, non-image data (e.g., tabular data and time series) are in fact more popular in real applications (e.g., medicine (Johnson et al., 2016) and finance (Takahashi et al., 2019) ). A survey conducted by Kaggle (Kaggle, 2017; van Breugel et al., 2023) revealed that 79% of the data scientists are mainly working on tabular data. Importantly, while image datasets are commonly of high quality, non-image data contain noisy samples in most cases. For example, sensor data are susceptible to measurement errors (Steinvall & Chevalier, 2005) , and such noise can significantly degrade the performance of diffusion models. To optimize the score model towards the score function, previous works (Song & Ermon, 2019; Song et al., 2021) derived the following score-matching loss: L " E pt,x0,xtq " λptqs θ pxptq, tq ´∇xptq ln p t pxptqq 2 2 ‰ ,