# Dynamic data generation and dynamic portfolio selection: an application of a score-based diffusion model

arXiv: https://arxiv.org/abs/2507.09916 · HTML: https://mlsanity.com/paper/2507.09916/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 6 of its 85 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Placed in

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

## Builds on (most cited first, 6 of 6)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [A Deep Reinforcement Learning Framework for the Financial Portfolio Management Problem](https://mlsanity.com/paper/1706.10059/) (2017)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [ScoreGrad: Multivariate Probabilistic Time Series Forecasting with Continuous Energy-based Generative Models](https://mlsanity.com/paper/2106.10121/) (2021)
- [Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networks](https://mlsanity.com/paper/2002.03938/) (2020)
- [Diffusion Factor Models: Generating High-Dimensional Returns with Factor Structure](https://mlsanity.com/paper/2504.06566/) (2025)

## Built on by (most cited first, 5 of 5)

- [Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance](https://mlsanity.com/paper/2509.03898/) (2025)
- [Generating solution paths of Markovian stochastic differential equations using diffusion models](https://mlsanity.com/paper/2509.08731/) (2025)
- [Diffusion Models for Adaptive Sequential Data Generation](https://mlsanity.com/paper/2606.06007/) (2026)
- [Factor-Based Conditional Diffusion Model for Contextual Portfolio Optimization](https://mlsanity.com/paper/2509.22088/) (2025)
- [Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian](https://mlsanity.com/paper/2605.19391/) (2026)

## Abstract (arXiv)

We study dynamic data generation and its application to model-free dynamic portfolio selection. Existing score-based diffusion models are typically designed to learn a static data distribution, whereas dynamic decision problems require generated trajectories that preserve the sequential information structure of the underlying process and support conditional sampling. To address this gap, we develop an adaptive score-based diffusion framework for dynamic data. Given samples from an unknown data-generating model mathbb P, the framework learns a generative model mathbb Q through conditional score matching and generates trajectories sequentially by updating the conditioning information over time. We establish quantitative error bounds between mathbb P and mathbb Q under the adapted Wasserstein metric mathcal Amathcal W2, which is tailored to nonanticipative dynamic problems, and show that the same adaptive sampling scheme provides conditional path generators. We then apply this dynamic data generation framework to dynamic mean-variance portfolio selection with limited historical price data. We prove stability of the dynamic mean-variance problem with respect to mathcal Amathcal W2, thereby translating the generative approximation error into performance control for portfolio policies. Building on these results, we implement a policy-gradient algorithm in the learned generative environment, where adaptively sampled paths serve as training scenarios. A synthetic ARMA experiment shows that the proposed adaptive sampling scheme generates distributions close to the true data-generating process. On real market data, the proposed approach outperforms several benchmarks, including the Markowitz portfolio, the equal-weight portfolio, and the S&P 500.