Trajectory Matching: Discrete Flow Matching with Structured Actions

TL;DR

Trajectory matching extends discrete flow matching by conditioning on full action sequences between start and end states, enabling complex, structured actions like fragment attachment or hierarchical growth. It overcomes limitations of factorized DFM by allowing non-independent, size-changing, and prerequisite-dependent operations without requiring simulation or factorization. The method achieves state-of-the-art results in molecular and tree generation, improving MOSES validity from 92.8% to 99.2%.

Why It Matters

This work significantly broadens the scope of discrete generative modeling by allowing users to define rich, domain-specific actions as part of the generative process. It enables more natural and efficient generation of structured data like molecules and trees, with direct transfer to substructure extension and linking tasks. The approach removes the need for simulation-based training and opens new avenues for action-aware generative AI.

Key Findings

• Trajectory matching enables principled training for complex, non-factorizable actions in discrete flow matching.
• It strictly subsumes factorized DFM and supports actions that change state size or depend on prior steps.
• Empirical results show superior performance on molecular and tree generation, with improved validity and transferability.