Markov Chain Monte Carlo with Diffusion Paths

arXiv:2607.11631 · stat.CO, stat.ML · Submitted 2026-07-13 · Read on arXiv

stat.CO, stat.ML

Submitted: 2026-07-13

Updated: 2026-09-12

Code: https://github.com/chenh77/mad-path

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Spectral Gap — 24× in this paper · explained in 5 episodes
• Trace — 10× in this paper · explained in 2 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• Normalizing Flow — 7× in this paper · explained in 3 episodes
• Generative Modeling — 5× in this paper · explained in 3 episodes
• Normalizing Flows — 5× in this paper · explained in 4 episodes
• Mode Collapse — 4× in this paper · explained in 2 episodes
• Score Function — 4× in this paper · explained in 4 episodes
• Diffusion Process — 3× in this paper · explained in 2 episodes
• Wasserstein Distance — 3× in this paper · explained in 4 episodes
• Diffusion Model — 2× in this paper · explained in 8 episodes
• Diffusion Models — 2× in this paper · explained in 6 episodes
• Diffusion Processes — 2× in this paper · explained in 2 episodes
• No-U-Turn Sampler — 2× in this paper
• 2-Wasserstein Distance — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Benchmark — 1× in this paper · explained in 2 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Clustering — 1× in this paper · explained in 2 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• Sparsity — 1× in this paper · explained in 4 episodes
• Stochastic Optimal Control (SOC) — 1× in this paper · explained in 2 episodes
• Uncertainty Quantification — 1× in this paper · explained in 8 episodes

Sources

• Bridge Matching Sampler: Scalable Sampling via Generalized Fixed-Point Diffusion Matching
• Target Score Matching
• Diffusion-based Annealed Boltzmann Generators : benefits, pitfalls and hopes
• No Trick, No Treat: Pursuits and Challenges Towards Simulation-free Training of Neural Samplers
• NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport
• Dynamical Measure Transport and Neural PDE Solvers for Sampling
• Comments on the holographic description of Narain theories

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