Underdamped diffusion samplers outperform traditional methods: researchers from Karlsruhe Institute of Technology, NVIDIA and ZUSE Institute Berlin have introduced a new framework for efficient sampling from complex distributions with complex distributions with degraded noise
The diffusion process has become a promising approach to sampling from complex distributions, but faces significant challenges when dealing with multimodal goals. Traditional methods based on excessive damping Langevin dynamics often show slow convergence rates when navigating between different modes of the distribution. Although the underdamped Langevin dynamics show empirical improvements by introducing additional momentum variables, there are fundamental limitations. In the inadequate model, Brownian motion couples indirectly with the degraded noise structure of spatial variables produce smoother paths, but theoretical analysis becomes complicated.
Existing methods such as using transition kernels such as annealing importance sampling (AIS) bridges and target distributions, while unadjusted Langevin annealing (ULA) achieves uncorrected overdamped Langevin dynamics within this framework. Monte Carlo diffusion (MCD) optimizes the goal to minimize marginal likelihood differences, while controlled Monte Carlo diffusion (CMCD) and sequentially controlled Langevin diffusion (SCLD) focus on kernel optimization with resampling strategies. Other methods specify backward transition cores, including path integral samplers (PIS), time-transformed diffusion samplers (DIS), and deoising diffusion samplers (DDS). Certain methods, such as diffusion bridge sampler (DB), learn forward and backward kernels independently.
Researchers from the NVIDIA KARLSRUHE Institute of Technology, the Zuse Institute, Dida Datenschmiede GmbH and the FZI Center for Information Technology Research have proposed a general framework for learning diffusion bridges to transport previous distributions to target distributions. This approach includes both existing diffusion models and water-depleted versions with degraded diffusion matrix, while noise affects only a specific dimension. The framework establishes a strict theoretical basis that suggests that score matching in unemployment is equivalent to maximizing the lower limit of probability. This approach solves the challenge of sampling from uneven density when direct samples from target distribution are unavailable.
The framework can perform comparative analysis between five sampling methods based on five critical diffusions: ULA, MCD, CMCD, DIS, and DBS. Unpopular variants of DIS and DBS represent new contributions to the field. The evaluation method used a diverse test bed, including seven high-dimensional sampling covering Bayesian inference tasks (credit, cancer, ionosphere, sonar), parametric inference problems (seeds, brownies) and Log Gaussian Cox Process (LGCP) with 1600 sizes. Furthermore, the synthesis benchmarks include challenging funnel distributions of regions with different concentration levels, providing rigorous testing for sampling methods for various dimensions and complexity profiles.
The results show that in real-world and synthetic benchmarks, underdamped Langevin dynamics always outperform the overdamped alternatives. Insufficient DBS Unpopular DBS exceeds the competition method even with less than 8 discrete steps. This efficiency translates into significant computational savings while maintaining excellent sampling quality. Regarding numerical integration solutions, professional integrators have significantly improved the classic Euler method for dynamics of insufficient damping. The OBAB and BAOAB schemes provide considerable performance without additional computational overhead, while the OBABO scheme still achieves the best overall results, although each discretization step requires a double evaluation of the control parameters.
In summary, this work establishes an integrated framework for diffusion bridges that encompasses degenerate stochastic processes. The unpopular diffusion bridge sampler achieves state-of-the-art results in multiple sampling tasks, with minimal high parameter tuning and several discrete steps. Thorough ablation studies confirm that performance improvements stem from the dynamics of underemployment, innovative numerical integrators, while learning a co-combination of forward and backward processes and end-to-end learning hyperparameters. Future directions include insufficient diffusion bridges using the lower bound on evidence derived in Lemma 2.4 (ELBO).
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The under-positioned diffusion sampler outperforms traditional methods: researchers from Karlsruhe Polytechnic, NVIDIA and ZUSE Institute Berlin have introduced a new framework for effective sampling of complex distributions from Demeneter Noise first emerged on Marktechpost.
