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

arXiv: https://arxiv.org/abs/2504.06566 · HTML: https://mlsanity.com/paper/2504.06566/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- First posted on arXiv 9 Apr 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Built on by (most cited first, 13 of 13)

- [Confidence-Based Decoding is Provably Efficient for Diffusion Language Models](https://mlsanity.com/paper/2603.22248/) (2026)
- [Dynamic data generation and dynamic portfolio selection: an application of a score-based diffusion model](https://mlsanity.com/paper/2507.09916/) (2025)
- [Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance](https://mlsanity.com/paper/2509.03898/) (2025)
- [Schr"odinger bridge for generative AI: Soft-constrained formulation and convergence analysis](https://mlsanity.com/paper/2510.11829/) (2025)
- [Diffusion Models Are Statistically Optimal for Learning Low-Dimensional Multi-Modal Distributions](https://mlsanity.com/paper/2605.30153/) (2026)
- [Generating solution paths of Markovian stochastic differential equations using diffusion models](https://mlsanity.com/paper/2509.08731/) (2025)
- [Tucker Diffusion Model for High-dimensional Tensor Generation](https://mlsanity.com/paper/2604.00481/) (2026)
- [Provably Reliable Classifier Guidance via Cross-Entropy Control](https://mlsanity.com/paper/2601.21200/) (2026)
- [Cold-Start Forecasting of New Product Life-Cycles via Conditional Diffusion Models](https://mlsanity.com/paper/2604.20370/) (2026)
- [On the Robustness of Distribution Support under Diffusion Guidance](https://mlsanity.com/paper/2605.07220/) (2026)
- [On the Limits of Latent Reuse in Diffusion Models](https://mlsanity.com/paper/2605.13448/) (2026)
- [Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimization](https://mlsanity.com/paper/2509.22088/) (2025)
- [Conditional Tensor Diffusion: Distributional Counterfactual Learning and Inference](https://mlsanity.com/paper/2609.25924/) (2026)

## Abstract (arXiv)

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. Our code is available at https://github.com/xymmmm00/diffusion_factor_model.