FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models

2026-09-28

AI Summary

This study addresses weight degeneracy in Feynman-Kac sequential Monte Carlo (SMC) for discrete diffusion model inference, where proposal-target misalignment limits sampling accuracy. We propose a training-free proposal control framework integrating graph-theoretic and quadratic programming tools to precisely compensate sparse jump-rate perturbations via a graph divergence term. By formulating a local convex objective that preserves target paths, we establish population stability and finite-particle convergence guarantees. Our approach significantly reduces reweighting variance and optimizes sampling trajectories. On continuous-time Markov chain benchmarks, terminal KL divergence improves by two orders of magnitude, while row-correlation mean squared error for Ising sampling decreases by a geometric mean factor of 5–7×, reaching up to 55× at peak.

Abstract

Many inference-time tasks for pretrained discrete diffusion models and diffusion language models reduce to drawing samples from a tilted version of the pretrained distribution. Feynman-Kac sequential Monte Carlo (SMC) makes this correction exact in principle, but its prescribed weights routinely degenerate when the proposal dynamics are misaligned with the tilt, capping the practical gains from additional particles. We introduce FluxLite, a lightweight, training-free proposal-control framework for discrete diffusion. On the sparse directed graph of pretrained reverse rates, any sparse jump-rate perturbation can be exactly compensated by a $q_t$-weighted graph-divergence term in the Feynman-Kac potential; the target path is therefore preserved while the residual reweighting variance becomes a local convex objective. We instantiate this principle as two practical samplers: a one-hop local reallocation rule (HEU) and a small nonnegative quadratic program over pretrained-rate bases (D-VCG). We further prove population stability under the standard score-entropy training loss, identifying a tilted-path coverage factor that governs robustness to score error, together with finite-particle convergence for a fixed controlled Feynman-Kac recursion. Empirically, FluxLite improves over standard Feynman-Kac SMC baselines by up to two orders of magnitude in terminal KL on an analytically tractable finite-state CTMC benchmark, and reduces row-correlation MSE on 2D Ising sampling by 5-7x in geometric mean and up to 55x at peak.

Problem

• discrete diffusion models
• Feynman-Kac SMC
• weight degeneracy
• proposal control
• inference-time sampling

Innovation

• Discrete Diffusion Models
• Feynman-Kac SMC
• Proposal Control
• Training-Free Sampling
• Sequential Monte Carlo