ART-MPG: Autoregressive R/T Manifold Path Guiding

Monte Carlo rendering and modern generative models both transform uncertain states into structured images, yet they are usually studied as separate processes. We introduce Monte Carlo Transport Scheduling, a framework that treats progressive path tracing as a continuous sampling-driven transport process. Our key observation is that the renderer already produces physically valid states along this process: nested Monte Carlo estimates trace a refinement trajectory whose natural time coordinate follows from sampling variance. This view leads to a continuous training framework that learns from real render endpoints rather than synthetic interpolants, preserving the statistical structure of Monte Carlo estimation while enabling arbitrary-step neural refinement. We evaluate the framework on a controlled rendering benchmark designed to separate transport difficulty from scene context, and show that it yields stable render refinement, supports continuous stopping between rendering states, and transfers as a physical prior for frozen generative samplers. These results suggest a common continuous-time substrate for rendering and generation, where Monte Carlo sampling provides both the physical states and the supervision for learning image transport.

Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the interaction order. This bottleneck limits its use in large-scale or real-time applications, forcing traditional tools to rely on heuristics that reduce path candidates at the cost of potentially reduced accuracy. To overcome this limitation, we propose a machine-learning-assisted framework that replaces exhaustive path searching with intelligent sampling via Generative Flow Networks. Applying these generative models to this domain presents challenges, particularly sparse rewards due to the rarity of valid paths, which can lead to convergence failures and trivial solutions when evaluating high-order interactions in complex environments. To ensure robust learning and efficient exploration, our framework incorporates three key components. First, an experience replay buffer captures and retains rare valid paths. Second, a uniform exploratory policy improves generalization and prevents overfitting to simple geometries. Third, a physics-based action masking strategy filters out physically impossible paths before the model considers them. Validated on idealized street-canyon scenarios, our model achieves substantial speedups over exhaustive search -- up to $10\times$ faster on GPU and $100\times$ faster on CPU -- while maintaining high coverage accuracy and successfully uncovering complex propagation paths. However, out-of-distribution evaluations on real-world Manhattan street geometries reveal that generalizing to substantially different urban morphologies requires further advancement in model capacity or alternative training strategies. Source code, tests, and a tutorial are available at https://github.com/jeertmans/sampling-paths.

Inference-time methods that aggregate and prune multiple samples have emerged as a powerful paradigm for steering large language models, yet we lack any principled understanding of their accuracy-cost tradeoffs. In this paper, we introduce a route to rigorously study such approaches using the lens of particle filtering algorithms such as Sequential Monte Carlo (SMC). Given a base language model and a process reward model estimating expected terminal rewards, we ask: how accurately can we sample from a target distribution given some number of process reward evaluations? Theoretically, we identify (1) simple criteria enabling non-asymptotic guarantees for SMC; (2) algorithmic improvements to SMC; and (3) a fundamental limit faced by all particle filtering methods. Empirically, we demonstrate that our theoretical criteria effectively govern the sampling error of SMC, though not necessarily its final accuracy, suggesting that theoretical perspectives beyond sampling may be necessary.