The paper introduces an amortized learning framework for selecting bandwidths in kernel density estimation by optimizing the logarithmic score across a distribution of tasks. It uses a truncated-and-renormalized bounded-support formulation and affine standardization to achieve stable learning and transferability across different intervals. Experiments on Gaussian samples, a multi-family benchmark, and randomized Gaussian mixtures demonstrate that the learned selector outperforms traditional methods such as Silverman’s rule, Sheather–Jones, and least‑squares cross‑validation, especially for small or heterogeneous samples.
By Junyi Liang, Hailiang Du
Product Monte Carlo (PMC) is an algorithm that estimates expectations under a product of densities using only Monte Carlo samples from each individual density. By reformulating the intractable product expectation as a regression problem involving computable conditional expectations, PMC provides both point estimates and coherent Bayesian uncertainty quantification. The method achieves higher accuracy, better-calibrated uncertainty, and improved scalability compared to existing techniques, and it does not require density evaluations, enabling its use in simulation‑based inference such as protein image analysis.
By Pietro Carlotti, Sifan Liu, Yuling Yao
arXiv:2601. 08136v2 Announce Type: replace Abstract: Diffusion and flow policies are gaining prominence in online reinforcement learning (RL) due to their expressive power, yet training them efficiently remains a critical challenge.
By Zeyang Li, Sunbochen Tang, Navid Azizan
The paper investigates training diffusion models to sample from distributions defined by unnormalized densities or energy functions. It benchmarks various diffusion-structured inference techniques, including simulation-based variational methods and off-policy approaches such as continuous generative flow networks, highlighting their relative strengths and challenging some prior claims. Additionally, the authors introduce a new exploration strategy for off-policy methods that employs local search in the target space with a replay buffer, demonstrating improved sample quality across multiple target distributions.
By Marcin Sendera, Minsu Kim, Sarthak Mittal, Pablo Lemos, Luca Scimeca, Jarrid Rector-Brooks, Alexandre Adam, Yoshua Bengio, Esmeralda S. Whitammer
The paper introduces a data‑free learning objective called relative trajectory balance for training diffusion models to sample from a posterior defined by a diffusion prior and an arbitrary black‑box constraint or likelihood. It proves asymptotic correctness of this objective and demonstrates its use across vision, language, and multimodal tasks, including classifier guidance, language infilling, and text‑to‑image generation. Additionally, the method is applied to continuous control with a score‑based behavior prior, achieving state‑of‑the‑art results in offline reinforcement learning.
By Siddarth Venkatraman, Moksh Jain, Luca Scimeca, Minsu Kim, Marcin Sendera, Mohsin Hasan, Luke Rowe, Sarthak Mittal, Pablo Lemos, Emmanuel Bengio, Alexandre Adam, Jarrid Rector-Brooks, Yoshua Bengio, Glen Berseth, Esmeralda S. Whitammer
arXiv:2605. 25811v2 Announce Type: replace-cross Abstract: We study counterfactual distribution learning for high-dimensional outcomes whose laws may concentrate near lower-dimensional structure.
By Kwangho Kim
BayesNDE is a neural density estimator that uses Bayesian generative modeling to estimate densities without relying on invertible networks or Jacobian-determinant calculations. It constructs an adaptive proposal for each observation by inferring a sample-specific latent posterior, and then applies bridge sampling to combine proposal samples with separate posterior samples for density estimation. Experiments on synthetic datasets show improved density estimation and structure recovery, while real-world applications demonstrate better anomaly detection.
By Chenglin Li, Qiao Liu
arXiv:2606. 15871v1 Announce Type: cross Abstract: Bayesian inference for inverse problems is run to evaluate integrals -- posterior expectations, tail probabilities, and risks -- across a stream of observations.
By Ali Siahkoohi
arXiv:2605. 13175v2 Announce Type: replace Abstract: Recent works have proposed incorporating heavy-tailed (HT) noise into diffusion- and flow-based generative models, with the goals of better recovering the tails of target distributions and improving generative diversity.
By Hamza Cherkaoui, H\'el\`ene Halconruy, Antonio Ocello
arXiv:2510. 11711v3 Announce Type: replace Abstract: This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions.
By Sanghyeok Choi, Sarthak Mittal, V\'ictor Elvira, Jinkyoo Park, Esmeralda S. Whitammer
arXiv:2504.05161v2 Announce Type: replace-cross
Abstract: Score estimation is the backbone of score-based generative models (SGMs), especially denoising diffusion probabilistic models (DDPMs). A key...
By Sinho Chewi, Alkis Kalavasis, Anay Mehrotra, Omar Montasser
arXiv:2606. 01002v1 Announce Type: cross Abstract: Engression is a recently proposed and effective framework for conditional distribution learning.
By Jiaqi Huang, Gongjun Xu, Ji Zhu