# Sampling Decisions: Exact Path-Space Control for Physics-Informed Generative Sampling

arXiv: https://arxiv.org/abs/2503.14549 · HTML: https://mlsanity.com/paper/2503.14549/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 6 of 6)

- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [Learning GFlowNets from partial episodes for improved convergence and stability](https://mlsanity.com/paper/2209.12782/) (2022)
- [Theoretical guarantees for sampling and inference in generative models with latent diffusions](https://mlsanity.com/paper/1903.01608/) (2019)
- [Discrete Probabilistic Inference as Control in Multi-path Environments](https://mlsanity.com/paper/2402.10309/) (2024)
- [Harmonic Path Integral Diffusion](https://mlsanity.com/paper/2409.15166/) (2024)

## Built on by (most cited first, 2 of 2)

- [DriftLite: Lightweight Drift Control for Inference-Time Scaling of Diffusion Models](https://mlsanity.com/paper/2509.21655/) (2025)
- [Sampling via Decision-Flow: Training-Free Extraction of Improved Latent Reasoning Paths in Large Language Models](https://mlsanity.com/paper/2609.12317/) (2026)

## Abstract (arXiv)

Scientific generative models must turn tractable local decisions into globally correlated samples that respect physical constraints. We introduce Sampling Decisions, a finite-horizon framework in which a structured object is assembled on a growing state graph and corrected globally by an exact path-space control law. For a prescribed Gibbs target, the corrected law is the unique relative-entropy projection of a sequential prior and is realized by a Doob h-transform with a linear backward desirability recursion. The same object admits equivalent interpretations as a KL-optimal controller, a one-sided Schrodinger transport, and an ideal value or flow function for autoregressive and GFlowNet-type generation. A route-resolved formulation yields a finite-particle algorithm, whose transition kernels and terminal law converge as the path budget grows. For binary graphical models, we prove a structural cancellation theorem: every fixed singleton-product prior disappears from the population correction, so improved one-point marginals do not alter the exact generative dynamics. The relevant information is conditional and prefix dependent. Statistical physics supplies this structure through a Local-Boltzmann prior that absorbs interactions as spins are revealed, while optimal path-space control supplies the missing look-ahead field from the unrevealed subgraph. On exactly enumerable Ising grids, this physics-informed proposal increases effective sample size by factors of about ten to nearly one thousand relative to product proposals and reaches the exact-target reference band at the tested budgets. On a larger 10*10 grid, beyond exact enumeration, the same hierarchy persists: Local-Boltzmann guidance avoids the severe weight collapse of product proposals and approaches a long-run MCMC baseline on the reported diagnostics.