[Paper Review] Diffusion-based Molecule Generation with Informative Prior Bridges

Lemeng Wu, Chengyue Gong+3 more|arXiv (Cornell University)|Sep 2, 2022

Cell Image Analysis Techniques19 citations

TL;DR

This paper proposes a novel framework for diffusion-based molecule and 3D point cloud generation by injecting physical and statistical priors through informative prior bridges—stochastic processes that guarantee terminal outputs matching desired data. Using a Lyapunov-based method to construct these bridges, the approach improves generation quality, stability, and point cloud uniformity, achieving state-of-the-art results with fewer sampling steps and efficient prior integration without architectural constraints.

ABSTRACT

AI-based molecule generation provides a promising approach to a large area of biomedical sciences and engineering, such as antibody design, hydrolase engineering, or vaccine development. Because the molecules are governed by physical laws, a key challenge is to incorporate prior information into the training procedure to generate high-quality and realistic molecules. We propose a simple and novel approach to steer the training of diffusion-based generative models with physical and statistics prior information. This is achieved by constructing physically informed diffusion bridges, stochastic processes that guarantee to yield a given observation at the fixed terminal time. We develop a Lyapunov function based method to construct and determine bridges, and propose a number of proposals of informative prior bridges for both high-quality molecule generation and uniformity-promoted 3D point cloud generation. With comprehensive experiments, we show that our method provides a powerful approach to the 3D generation task, yielding molecule structures with better quality and stability scores and more uniformly distributed point clouds of high qualities.

Motivation & Objective

• To address the challenge of incorporating strong physical and statistical priors into diffusion-based generative models for molecule and 3D point cloud generation.
• To develop a flexible, architecture-agnostic method for prior injection that improves generation quality and stability without modifying model structure.
• To enable uniform, high-quality 3D point cloud generation by embedding uniformity-promoting forces into the diffusion process.
• To provide a systematic, Lyapunov-based method for constructing diffusion bridges that guarantee terminal outputs.
• To demonstrate state-of-the-art performance in molecule generation and point cloud uniformity with reduced sampling steps.

Proposed method

• Constructs diffusion bridges as stochastic processes that deterministically yield a given data point at a fixed terminal time, ensuring prior-informed generation.
• Employs a Lyapunov function-based approach to systematically design and determine the drift terms of the bridges, enabling stable and interpretable prior integration.
• Introduces energy functions—Riesz potential and statistic gap energy—for promoting uniform point distribution in 3D generation tasks.
• Applies physics-informed energy functions (e.g., bond length, angle, and torsion potentials) to guide molecule generation while preserving generative flexibility.
• Trains the neural diffusion model to imitate the prior bridges, effectively steering the reverse process toward realistic, high-quality outputs.
• Uses a joint learning scheme where the bridge parameters (e.g., α) are optimized end-to-end with the diffusion model.

Experimental results

Research questions

• RQ1 Can informative prior bridges significantly improve the quality and stability of diffusion-based molecule generation without architectural modifications?
• RQ2 How can physical and statistical priors be systematically embedded into the diffusion process to guide generation toward realistic and uniform outputs?
• RQ3 Can prior-informed bridges reduce sampling steps while maintaining or improving generation quality in 3D point cloud generation?
• RQ4 How do different prior forces (e.g., Riesz vs. statistic gap energy) affect point cloud uniformity and shape realism?
• RQ5 What is the impact of prior integration via bridges on training efficiency and convergence speed compared to standard diffusion models?

Key findings

• The proposed method achieves state-of-the-art performance in molecule generation, outperforming existing physics-informed baselines in both quality and stability metrics.
• With only 10 diffusion steps, the method matches or exceeds the performance of standard diffusion models trained with 100 steps, demonstrating faster convergence.
• The inclusion of Riesz energy and statistic gap energy in the bridge process leads to significantly more uniformly distributed point clouds, with the latter showing better robustness.
• In the 100-step setup, the method with prior bridges outperforms the baseline diffusion model on both MMD and COV metrics across all evaluated categories.
• The method achieves high-quality, stable molecule generation by injecting prior knowledge directly into the training process, avoiding the need for architectural constraints.
• Visualization results confirm that prior-informed bridges produce more realistic and evenly distributed point clouds, with Riesz energy occasionally introducing outliers due to strong repulsion.