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[2602.17211] MGD: Moment Guided Diffusion for Maximum Entropy Generation
Summary
The paper introduces Moment Guided Diffusion (MGD), a novel method for generating maximum entropy distributions by guiding moments toward specified values, improving efficiency in high-dimensional sampling.
Why It Matters
MGD addresses the limitations of classical maximum entropy methods and generative models by combining their strengths. This advancement is significant for fields requiring effective sampling from limited data, such as finance and cosmology, enhancing both theoretical understanding and practical applications.
Key Takeaways
- MGD combines maximum entropy methods with diffusion models for efficient sampling.
- The method avoids slow mixing issues common in traditional sampling techniques.
- MGD shows convergence to maximum entropy distributions under specific conditions.
- Applications include financial time series and turbulent flow analysis.
- The approach provides a tractable estimator for entropy from dynamic processes.
Statistics > Machine Learning arXiv:2602.17211 (stat) [Submitted on 19 Feb 2026] Title:MGD: Moment Guided Diffusion for Maximum Entropy Generation Authors:Etienne Lempereur, Nathanaël Cuvelle--Magar, Florentin Coeurdoux, Stéphane Mallat, Eric Vanden-Eijnden View a PDF of the paper titled MGD: Moment Guided Diffusion for Maximum Entropy Generation, by Etienne Lempereur and 4 other authors View PDF HTML (experimental) Abstract:Generating samples from limited information is a fundamental problem across scientific domains. Classical maximum entropy methods provide principled uncertainty quantification from moment constraints but require sampling via MCMC or Langevin dynamics, which typically exhibit exponential slowdown in high dimensions. In contrast, generative models based on diffusion and flow matching efficiently transport noise to data but offer limited theoretical guarantees and can overfit when data is scarce. We introduce Moment Guided Diffusion (MGD), which combines elements of both approaches. Building on the stochastic interpolant framework, MGD samples maximum entropy distributions by solving a stochastic differential equation that guides moments toward prescribed values in finite time, thereby avoiding slow mixing in equilibrium-based methods. We formally obtain, in the large-volatility limit, convergence of MGD to the maximum entropy distribution and derive a tractable estimator of the resulting entropy computed directly from the dynamics. Applications to financ...
