Graph Forward Distribution Matching for Molecular Inverse Design
cs.LG
Submitted: 2026-09-25
Updated: 2026-09-25
License: http://creativecommons.org/licenses/by/4.0/
The gist: Achieving precise control over multiple properties without sacrificing chemical validity remains a central challenge in molecular inverse design.
Terminology
Abstract
Achieving precise control over multiple properties without sacrificing chemical validity remains a central challenge in molecular inverse design. Existing reinforcement learning (RL) methods fine-tune graph diffusion models by treating **reverse** sampling as a sequential policy, using a single terminal reward to optimize hundreds of coupled decisions. They often suffer from instability, validity collapse, and limited property gains. We introduce GraphFDM (Graph Forward Distribution Matching), a new online RL paradigm for graph diffusion that performs optimization through the **forward** process. GraphFDM uses valid generations to define a reward-tilted target distribution jointly optimized over graph size and molecular structure for each property condition, incorporating reinforcement signals into supervised learning without storing reverse trajectories. We derive the unique optimal target, prove a condition-wise improvement guarantee, and show that the fixed graph-size prior of standard graph diffusion leaves an irreducible matching gap. In multi-conditional polymer and small-molecule generation, GraphFDM achieves the lowest MAE on every target property, with reductions of up to 53.0% relative to the strongest baselines and chemical validity above 0.99. It further generalizes to out-of-distribution property combinations.
Sources
- Training Diffusion Models with Reinforcement Learning
- MolGuidance: Advanced Guidance Strategies for Conditional Molecular Generation with Flow Matching
- Graph Diffusion Policy Optimization
- Classifier-free graph diffusion for molecular property targeting
- Graph Diffusion that can Insert and Delete
- DeFoG: Discrete Flow Matching for Graph Generation
- Steering Masked Discrete Diffusion Models via Discrete Denoising Posterior Prediction
- MARS: Markov Molecular Sampling for Multi-objective Drug Discovery
- Graph-GRPO: Training Graph Flow Models with Reinforcement Learning
- Controllable Molecular Generative Foundation Models
- Enhancing Reasoning for Diffusion LLMs via Distribution Matching Policy Optimization
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