Generating Synthetic Stock Return Distributions with Diffusion Models

Modeling the probability distribution of stock returns is a fundamental challenge in quantitative finance, with significant implications for risk management, derivative pricing, and portfolio optimization. This paper proposes a diffusion-based generative framework tailored to the statistical characteristics of financial return distributions. By incorporating learned reverse-process variance, velocity parameterization, and a sigmoid noise schedule, the proposed model aims to improve distributional fidelity, particularly in the tails. The framework is further extended to regime-conditional generation, enabling controlled simulation of distinct market states. Empirical evaluations demonstrate that the proposed approach outperforms classical parametric models such as Geometric Brownian Motion and GARCH, deep generative baselines like VAEs, and existing diffusion-based methods across multiple distributional metrics, including higher-order moments and tail behaviors. The results highlight the potential of diffusion models as robust tools for synthetic return generation and scenario analysis in finance.