Factor-Based Conditional Diffusion Model for Portfolio Optimization

ArXiv ID: 2509.22088 “View on arXiv”

Authors: Xuefeng Gao, Mengying He, Xuedong He

Abstract

We propose a novel conditional diffusion model for portfolio optimization that learns the cross-sectional distribution of next-day stock returns conditioned on asset-specific factors. The model builds on the Diffusion Transformer with token-wise conditioning, linking each asset’s return to its own factor vector while capturing cross-asset dependencies. Generated return samples are used for daily mean-variance optimization under realistic constraints. Empirical results on the Chinese A-share market show that our approach consistently outperforms benchmark methods based on standard empirical and shrinkage-based estimators across multiple metrics.

Keywords: Conditional diffusion model, Diffusion Transformer, Portfolio optimization, Mean-variance optimization, Cross-sectional distribution, Equities (Chinese A-share)

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced generative modeling (diffusion models) with substantial mathematical foundations and novel conditioning mechanisms, while providing detailed empirical backtesting on real financial data with performance metrics and transaction cost considerations.

  flowchart TD
    A["Research Goal: <br>Develop novel method for daily <br>Chinese A-share portfolio returns"] --> B["Methodology: <br>Factor-Based Conditional Diffusion Model"]
    B --> C["Data Input: <br>Chinese A-share market data <br>+ Asset-specific factor vectors"]
    C --> D["Computation: <br>Conditional Diffusion Process <br>(Diffusion Transformer) <br>Generate return samples"]
    D --> E["Optimization: <br>Daily Mean-Variance Optimization <br>with realistic constraints"]
    E --> F["Outcome: <br>Consistent outperformance <br>vs. benchmark methods <br>(empirical & shrinkage estimators)"]