This paper presents a practical application of Relative Trajectory Balance (RTB), a recently introduced off-policy reinforcement learning (RL) objective that can asymptotically solve Bayesian inverse problems optimally. We extend the original work by using RTB to train conditional diffusion model posteriors from pretrained unconditional priors for challenging linear and non-linear inverse problems in vision, and science. We use the objective alongside techniques such as off-policy backtracking exploration to improve training. Importantly, our results show that existing training-free diffusion posterior methods struggle to perform effective posterior inference in latent space due to inherent biases.

Inferring sky surface brightness distributions from noisy interferometric data in a principled statistical framework has been a key challenge in radio astronomy. In this work, we introduce Imaging for Radio Interferometry with Score-based models (IRIS). We use score-based models trained on optical images of galaxies as an expressive prior in combination with a Gaussian likelihood in the uv-space to infer images of protoplanetary disks from visibility data of the DSHARP survey conducted by ALMA. We demonstrate the advantages of this framework compared with traditional radio interferometry imaging algorithms, showing that it produces plausible posterior samples despite the use of a misspecified galaxy prior. Through coverage testing on simulations, we empirically evaluate the accuracy of this approach to generate calibrated posterior samples.

With advancements in generative models, evaluating their performance using rigorous, clearly defined metrics and We propose a comprehensive sample-based criteria has become increasingly essential. Disambiguating method for assessing the quality of generative true from modeled distributions is especially pertinent in models. The proposed approach enables the estimation light of the growing emphasis on AI safety within the community, of the probability that two sets of samples as well as in scientific domains where stringent standards are drawn from the same distribution, providing of rigor and uncertainty quantification are needed for a statistically rigorous method for assessing the the adoption of machine learning methods. When evaluating performance of a single generative model or the generative models, we are interested in three qualitative comparison of multiple competing models trained properties (Stein et al., 2023; Jiralerspong et al., 2023): Fidelity on the same dataset. This comparison can be conducted refers to the quality and realism of individual outputs by dividing the space into non-overlapping generated by a model. It assesses how indistinguishable regions and comparing the number of data samples each generated sample is from real data.

Gaussian noise was then added to produce a noisy simulated data. Given the data, the posterior of a model (a pixelated image of the undistorted background source) could be calculated by adding the likelihood and the prior terms. Furthermore since the model is perfectly linear (and known) and the noise and the prior are Gaussian, the posterior is a high-dimensional Gaussian posterior that could be calculated analytically, allowing us to compare the samples drawn with GGNS with the analytic solution. Figure 2 shows a comparison between the true image, and its noise, and the one recovered by GGNS. We see that we can recover both the correct image, and the noise distribution. We emphasize that this is a uni-modal problem and that the experiment's goal is to demonstrate the capability of GGNS to sample in high dimensions (in this case, 256), such as images, and to test the agreement between the samples and a baseline analytic solution.

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 semisupervised 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. Anomaly detection seeks to identify observations that differ from the others to such a large extent that they are likely generated by a different mechanism (Hawkins, 1980). This is a longstanding research problem in machine learning with applications in various fields ranging from medicine (Pachauri & Sharma, 2015; Salem et al., 2013), finance (Ahmed et al., 2016b), security (Ahmed et al., 2016a), manufacturing (Susto et al., 2017), particle physics (Fraser et al., 2022) and geospatial data (Yairi et al., 2006). Despite its significance and potential for impact (e.g., leading to the discovery of new phenomena), to this day traditional anomaly detection methods, such as nearest neighbours, reportedly outperform deep learning techniques on various benchmarks (Han et al., 2022) by a significant margin.

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. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. 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.

Inferring accurate posteriors for high-dimensional representations of the brightness of gravitationally-lensed sources is a major challenge, in part due to the difficulties of accurately quantifying the priors. Here, we report the use of a score-based model to encode the prior for the inference of undistorted images of background galaxies. This model is trained on a set of high-resolution images of undistorted galaxies. By adding the likelihood score to the prior score and using a reverse-time stochastic differential equation solver, we obtain samples from the posterior. Our method produces independent posterior samples and models the data almost down to the noise level. We show how the balance between the likelihood and the prior meet our expectations in an experiment with out-of-distribution data.