We propose a likelihood-free method for comparing two distributions given samples from each, with the goal of assessing the quality of generative models. The proposed approach, PQMass, provides a statistically rigorous method for assessing the performance of a single generative model or the comparison of multiple competing models. PQMass divides the sample space into non-overlapping regions and applies chi-squared tests to the number of data samples that fall within each region, giving a $p$-value that measures the probability that the bin counts derived from two sets of samples are drawn from the same multinomial distribution. PQMass does not depend on assumptions regarding the density of the true distribution, nor does it rely on training or fitting any auxiliary models. We evaluate PQMass on data of various modalities and dimensions, demonstrating its effectiveness in assessing the quality, novelty, and diversity of generated samples. We further show that PQMass scales well to moderately high-dimensional data and thus obviates the need for feature extraction in practical applications.

Known for their impressive performance in generative modeling, diffusion models are attractive candidates for density-based anomaly detection. This paper investigates different variations of diffusion modeling for unsupervised and semi-supervised anomaly detection. In particular, we find that Denoising Diffusion Probability Models (DDPM) are performant on anomaly detection benchmarks yet computationally expensive. By simplifying DDPM in application to anomaly detection, we are naturally led to an alternative approach called Diffusion Time Estimation (DTE). DTE estimates the distribution over diffusion time for a given input and uses the mode or mean of this distribution as the anomaly score. We derive an analytical form for this density and leverage a deep neural network to improve inference efficiency. Through empirical evaluations on the ADBench benchmark, we demonstrate that all diffusion-based anomaly detection methods perform competitively for both semi-supervised and unsupervised settings. Notably, DTE achieves orders of magnitude faster inference time than DDPM, while outperforming it on this benchmark. These results establish diffusion-based anomaly detection as a scalable alternative to traditional methods and recent deep-learning techniques for standard unsupervised and semi-supervised anomaly detection settings.

We present a performant, general-purpose gradient-guided nested sampling (GGNS) algorithm, combining the state of the art in differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization. This unique combination allows GGNS to scale well with dimensionality and perform competitively on a variety of synthetic and real-world problems. We also show the potential of combining nested sampling with generative flow networks to obtain large amounts of high-quality samples from the posterior distribution. This combination leads to faster mode discovery and more accurate estimates of the partition function.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Posterior inference with generative models is an alternative to methods such as Markov Chain Monte Carlo, both for likelihood-based and simulation-based inference. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce "Tests of Accuracy with Random Points" (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.