aiqbench analysis
This research proposes reformulating reverse-time diffusion samplers as forward-backward stochastic differential equations (FBSDEs), eliminating the need for separate score pre-estimation in generative modeling tasks where target densities are known only up to a normalizing constant. The study mathematically proves equivalence between these formulations and provides an error decomposition that accounts for Gaussian initialization, Euler discretization, and approximate FBSDE solving. Experimental results on complex synthetic distributions validate the method's potential efficiency for sampling from targets with intricate global structures.
A Reverse-BSDE Diffusion Sampler
arXiv:2505.06800v2 Announce Type: replace-cross Abstract: Diffusion-based generative models have renewed interest in stochastic differential equation methods for sampling from complex distributions. We study a setting in which the target density is known only up to a normalizing constant and reformulate the reverse-time diffusion sampler as a forward-backward stochastic differential equation (FBSDE). This formulation replaces the separate pre-estimation of the time-dependent score with the solution of a coupled stochastic system. We prove the equivalence of these formulations and provide a decomposition of the approximation error arising from initializing the sampler with a standard Gaussian, applying Euler discretization to the dynamics, and solving the FBSDE approximately. We then evaluate the proposed algorithm on synthetic targets, including separated mixtures, anisotropic Gaussian distributions, and banana-shaped and ring-shaped distributions. The results demonstrate the promise of the method, particularly for targets with complex global structure.
Abstract:Diffusion-based generative models have renewed interest in stochastic differential equation methods for sampling from complex distributions. We study a setting in which the target density is known only up to a normalizing constant and reformulate the reverse-time diffusion sampler as a forward-backward stochastic differential equation (FBSDE). This formulation replaces the separate pre-estimation of the time-dependent score with the solution of a coupled stochastic system. We prove the equivalence of these formulations and provide a decomposition of the approximation error arising from initializing the sampler with a standard Gaussian, applying Euler discretization to the dynamics, and solving the FBSDE approximately. We then evaluate the proposed algorithm on synthetic targets, including separated mixtures, anisotropic Gaussian distributions, and banana-shaped and ring-shaped distributions. The results demonstrate the promise of the method, particularly for targets with complex global structure.
Machine Learning (stat.ML); Machine Learning (cs.LG); Probability (math.PR)
arXiv:2505.06800 [stat.ML]
(or arXiv:2505.06800v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2505.06800 Focus to learn more arXiv-issued DOI via DataCite
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