dida at ICML: Lorenz presents two papers on diffusion-based Sampling

Our founder and managing director Lorenz Richter presented two papers on diffusion-based sampling at the International Conference on Machine Learning (ICML) in Seoul this year, both appearing in the poster sessions.

The first, "Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching," introduces a method (BMS) for sampling from unnormalized densities. It frames prior matching objectives as special cases of fixed-point iterations rooted in Nelson's relation, which lets it learn a stochastic transport map between an arbitrary prior and target with a single, stable objective and a damped variant helps mitigate mode collapse during training.

The second, "Tensor Train Diffusion: Leveraging Low-Rank Structures for High-Dimensional Score-Based Sampling," tackles the Hamilton-Jacobi-Bellman equation that governs the score in a diffusion process. Rather than relying on PINNs or trajectory-based solvers, it uses the functional tensor train format to exploit latent low-rank structure, giving a faster and more robust sampler in high dimensions.

Both papers sit squarely in our work at the intersection of mathematics and machine learning, and drew good conversations and a good turnout at the boards.