Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure
Prof. Ruixun ZHANG
Associate Professor, Department of Financial Mathematics,
School of Mathematical Sciences
Peking University
Date: 9 January 2026 (Friday)
Time: 10:30-12:00
Venue: E22-2015
Host: Prof. Yi DING, Assistant Professor in Business Economics
Abstract
Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that integrates latent factor structure into generative diffusion processes, bridging econometrics with modern generative AI to address the challenges of the curse of dimensionality and data scarcity in financial simulation. By exploiting the low-dimensional factor structure inherent in asset returns, we decompose the score function–a key component in diffusion models–using time-varying orthogonal projections, and this decomposition is incorporated into the design of neural network architectures. We derive rigorous statistical guarantees, establishing nonasymptotic error bounds for both score estimation at O(d^{5/2} n^{-2/(k+5)}) and generated distribution at O(d^{5/4} n^{-1/2(k+5)}), primarily driven by the intrinsic factor dimension k rather than the number of assets d, surpassing the dimension-dependent limits in the classical nonparametric statistics literature and making the framework viable for markets with thousands of assets. Numerical studies confirm superior performance in latent subspace recovery under small data regimes. Empirical analysis demonstrates the economic significance of our framework in constructing mean-variance optimal portfolios and factor portfolios. This work presents the first theoretical integration of factor structure with diffusion models, offering a principled approach for high-dimensional financial simulation with limited data.
Speaker
Prof. Ruixun ZHANG is an associate professor with tenure in the Department of Financial Mathematics, School of Mathematical Sciences at Peking University. Ruixun received a Ph.D. in Applied Mathematics from MIT in 2015, and bachelor’s degrees in Mathematics and Applied Mathematics, and Economics (double degree) from Peking University in 2011. Ruixun’s research interests include machine learning, sustainable investing, market microstructure, and evolutionary models of financial behavior. His research has received several best paper awards, and has appeared in journals such as Proceedings of the National Academy of Sciences, Operations Research, Management Science, and Journal of the American Statistical Association.
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