Fixed-Point Bridge Matching Makes Diffusion Sampling Scalable Without Target Data
Lorenz Richter’s seminar argues for a non-Markovian route to diffusion-based sampling when the target distribution is known only through an unnormalized density rather than data. He presents existing Markovian path-space samplers as theoretically flexible but increasingly constrained by trajectory simulation and storage costs, then proposes building reciprocal bridge measures from endpoint couplings and learning their Markovian projection by fixed-point regression. The resulting Bridge Matching Sampler, Richter says, uses a single learned control, accommodates flexible priors and reference processes, and shows improved stability and mode preservation in high-dimensional synthetic and molecular benchmarks, especially with damping.
Microsoft Research·May 26, 2026·18 min read
