FluxLite：离散扩散模型的推理时提议控制
FluxLite: Inference-Time Proposal Control for Discrete Diffusion Models
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中文总结 AI 辅助
FluxLite 提出一种无需训练的离散扩散模型推理时提议控制框架，通过 Feynman-Kac 势中的图散度补偿扰动，实现精确校正，显著提升采样质量。
中文摘要 AI 辅助
许多针对预训练离散扩散模型和扩散语言模型的推理时任务，可归结为从预训练分布的倾斜版本中抽取样本。Feynman-Kac 序贯蒙特卡洛（SMC）原则上能使这种校正精确，但当提议动力学与倾斜方向不一致时，其规定的权重通常会退化，从而限制了增加粒子数带来的实际收益。我们提出 FluxLite，一个轻量级、无需训练的离散扩散提议控制框架。在预训练反向速率的稀疏有向图上，任何稀疏跳变率扰动都可以通过 Feynman-Kac 势中的 $q_t$ 加权图散度项精确补偿；因此目标路径得以保留，而残余重加权方差成为局部凸目标。我们将这一原理实例化为两种实用采样器：一跳局部重分配规则（HEU）和在预训练速率基上的小型非负二次规划（D-VCG）。我们进一步证明了在标准分数熵训练损失下的总体稳定性，识别出一个倾斜路径覆盖因子，该因子控制对分数误差的鲁棒性，以及固定受控 Feynman-Kac 递归的有限粒子收敛性。实验上，FluxLite 在解析可处理的有限状态 CTMC 基准上，将终端 KL 相比标准 Feynman-Kac SMC 基线提升最多两个数量级，并在二维 Ising 采样中将行相关 MSE 的几何均值降低 5-7 倍，峰值降低最多 55 倍。
英文摘要
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.
发表机构
- Kempner Institute（肯普纳研究所）
- Harvard University（哈佛大学）
- ICME（计算与数学工程研究所）
- Stanford University（斯坦福大学）
- Department of Chemistry（化学系）
- Center for Computational Mathematics（计算数学中心）
- Flatiron Institute（熨斗研究所）
- Department of Mathematics（数学系）
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