Diffusion Models

Most generative models for time series—particularly those borrowed from image generation—treat financial prices like any other numerical data: throw in Gaussian noise, then learn to clean it up. But markets aren’t like pixels. Financial time series have unique structures: they evolve multiplicatively, exhibit heteroskedasticity, and follow stochastic dynamics that traditional diffusion models ignore. In this week’s standout paper, “A diffusion-based generative model for financial time series via geometric Brownian motion,” Kim et al. propose a subtle yet profound twist: model the noise using financial theory, specifically geometric Brownian motion (GBM), rather than injecting it naively. ...

What if you could simulate thousands of realistic futures for the market, all conditioned on what’s happening today—and then train an investment strategy on those futures? That’s the central idea behind a bold new approach to portfolio optimization that blends score-based diffusion models with reinforcement learning, and it’s showing results that beat classic benchmarks like the S&P 500 and traditional Markowitz portfolios. ...