Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure

2025-04-09

AI Summary

To address the challenges of financial asset return simulation and poor interpretability in high-dimensional, low-sample-size settings, this paper proposes a diffusion-based generative model embedded with classical factor structure. Methodologically, latent factor dynamics are integrated into the diffusion process, and the score function is decomposed into a low-dimensional subspace via time-varying orthogonal projection, reducing modeling complexity from the asset dimension $d$ to the intrinsic factor dimension $k ll d$. Theoretically, we establish the first unified framework linking factor models and diffusion generative modeling, and derive non-asymptotic error bounds—thereby circumventing the curse of dimensionality inherent in conventional nonparametric statistics. Empirically, the model significantly improves accuracy in recovering latent factor spaces and robustly constructs mean-variance optimal portfolios and economically interpretable factor-based portfolios—even under small-sample regimes—achieving both statistical efficiency and financial meaningfulness.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Addressing high-dimensional financial returns simulation challenges
• Integrating factor structure into generative diffusion processes
• Overcoming dimensionality and data scarcity in finance

Innovation

• Integrates latent factor structure into diffusion processes
• Decomposes score function via time-varying orthogonal projections
• Derives nonasymptotic error bounds for high-dimensional simulation