Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Models

Score-based diffusion models (SBDMs) are powerful amortized samplers for Boltzmann distributions; however, imperfect score estimates bias downstream Monte Carlo estimates. Classical importance sampling (IS) can correct this bias, but computing exact likelihoods requires solving the probability-flow ordinary differential equation (PF-ODE), a procedure that is prohibitively costly and scales poorly with dimensionality. We introduce Variance-Tuned Diffusion Importance Sampling (VT-DIS), a lightweight post-training method that adapts the per-step noise covariance of a pretrained SBDM by minimizing the $\alpha$-divergence ($\alpha=2$) between its forward diffusion and reverse denoising trajectories. VT-DIS assigns a single trajectory-wise importance weight to the joint forward-reverse process, yielding unbiased expectation estimates at test time with negligible overhead compared to standard sampling. On the DW-4, LJ-13, and alanine-dipeptide benchmarks, VT-DIS achieves effective sample sizes of approximately 80 %, 35 %, and 3.5 %, respectively, while using only a fraction of the computational budget required by vanilla diffusion + IS or PF-ODE-based IS.

Exploring Pseudo-Token Approaches in Transformer Neural Processes

Neural Processes (NPs) have gained attention in meta-learning for their ability to quantify uncertainty, together with their rapid prediction and adaptability. However, traditional NPs are prone to underfitting. Transformer Neural Processes (TNPs) significantly outperform existing NPs, yet their applicability in real-world scenarios is hindered by their quadratic computational complexity relative to both context and target data points. To address this, pseudo-token-based TNPs (PT-TNPs) have emerged as a novel NPs subset that condense context data into latent vectors or pseudo-tokens, reducing computational demands. We introduce the Induced Set Attentive Neural Processes (ISANPs), employing Induced Set Attention and an innovative query phase to improve querying efficiency. Our evaluations show that ISANPs perform competitively with TNPs and often surpass state-of-the-art models in 1D regression, image completion, contextual bandits, and Bayesian optimization. Crucially, ISANPs offer a tunable balance between performance and computational complexity, which scale well to larger datasets where TNPs face limitations.

Efficient and Unbiased Sampling of Boltzmann Distributions via Consistency Models

Diffusion models have shown promising potential for advancing Boltzmann Generators. However, two critical challenges persist: (1) inherent errors in samples due to model imperfections, and (2) the requirement of hundreds of functional evaluations (NFEs) to achieve high-quality samples. While existing solutions like importance sampling and distillation address these issues separately, they are often incompatible, as most distillation models lack the necessary density information for importance sampling. This paper introduces a novel sampling method that effectively combines Consistency Models (CMs) with importance sampling. We evaluate our approach on both synthetic energy functions and equivariant n-body particle systems. Our method produces unbiased samples using only 6-25 NFEs while achieving a comparable Effective Sample Size (ESS) to Denoising Diffusion Probabilistic Models (DDPMs) that require approximately 100 NFEs.