Outlier Generation in Diffusion Models

The growing prevalence of anomalous events in real-world data highlights the importance of synthetic data generation techniques capable of identifying and generating outliers. This research introduces a novel approach for generating controlled outliers in score-based generative models by modifying diffusion model dynamics. We propose incorporating a drift control term to the reverse stochastic differential equation (SDE) with regularization inspired by Girsanov’s theorem to directly influence the evolution of data likelihood, allowing precise control over the generation of outliers.
Our method leverages the Fokker-Planck-Kolmogorov (FPK) equation to describe the evolution of data likelihood in the presence of control functions. Given the computational challenges of stochastic control, we investigate optimal transport-inspired evolution of likelihood to maintain generation stability while enforcing outlier behavior. We explore practical approaches such as quadratic programming (QP) to derive interpretable and formally verifiable closed-form control functions.
We plan to validate our approach through numerical experiments on a mixture of Gaussians, employing analytical score functions to assess the effectiveness of controlled likelihood steering. This approach will then be extended to tabular data. Our evaluation focuses on the ability of this method to generate diverse and realistic outliers while preserving the fundamental properties of the diffusion model.

Faculty Supervisor:

Jun Liu

Student:

Partner:

Royal Bank of Canada (Borealis)

Discipline:

Computer science

Sector:

Artificial Intelligence

University:

University of Waterloo

Program: