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Rare events such as conformational changes in biomolecules, phase transitions, and chemical reactions are central to the behavior of many physical systems, yet they are extremely difficult to study computationally because unbiased simulations seldom produce them. Transition Path Theory (TPT) provides a rigorous statistical framework for analyzing such events: it characterizes the ensemble of reactive trajectories between two designated metastable states (reactant and product), and its central object--the committor function, which gives the probability that the system will next reach the product rather than the reactant--encodes all essential kinetic and thermodynamic information. We introduce a framework that casts committor estimation as a stochastic optimal control (SOC) problem. In this formulation the committor defines a feedback control--proportional to the gradient of its logarithm--that actively steers trajectories toward the reactive region, thereby enabling efficient sampling of reactive paths. To solve the resulting hitting-time control problem we develop two complementary objectives: a direct backpropagation loss and a principled off-policy Value Matching loss, for which we establish first-order optimality guarantees. We further address metastability, which can trap controlled trajectories in intermediate basins, by introducing an alternative sampling process that preserves the reactive current while lowering effective energy barriers. On benchmark systems, the framework yields markedly more accurate committor estimates, reaction rates, and equilibrium constants than existing methods. The talk will mostly cover the manuscript https://arxiv.org/abs/2604.13213.

This talk introduces diffusion for language and the research advances that underlie modern diffusion LLMs. We describe the building blocks of today's leading open-source models, starting from simple masked diffusion language modeling (MDLM), and covering techniques for iterative refinement, controllable generation, and efficient inference with variable-length sequences. These techniques unlock capabilities autoregressive models lack: fast generation at >1000 tokens/second, new forms of inference-time scaling through repeated refinement, and fine-grained controllable generation that has proven especially valuable in the sciences. We ground these in the context of leading models for biological sequences (proteins and DNA) and natural language, including frontier diffusion LLMs like Nemotron Diffusion, Gemma Diffusion, and Mercury 2.

I will talk about Signed Rectified Flow (Signed RF), a generalization of Rectified Flow that targets a signed measure of the form (1+a)p_+ - ap_-, where a>0, p_+ represents the distribution to promote, and p_- represents the distribution to suppress. Although sampling from a signed measure is not well-defined, Signed RF induces a valid generative process that concentrates on the positive region of the signed measure while provably excluding regions dominated by the negative component. This yields a principled framework for incorporating negative information and exclusion constraints into generative modeling. Theoretically, we analyze the underlying signed continuity equation and explain how negative mass creates exclusion barriers through a charged-particle interpretation. Empirically, we find that Signed RF enables practical algorithms for injecting both positive and negative information into generative flows, leading to higher-quality, less memorized, and safer generation.