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Symmetry is ubiquitous in many real-world phenomena and tasks, such as physics, images, and molecular simulations. Empirical studies have demonstrated that incorporating symmetries into generative models can provide better generalization…

Machine Learning · Statistics 2026-05-12 Ziyu Chen , Markos A. Katsoulakis , Benjamin J. Zhang

Many forecasts consist not of point predictions but concern the evolution of quantities. For example, a central bank might predict the interest rates during the next quarter, an epidemiologist might predict trajectories of infection rates,…

Methodology · Statistics 2021-11-12 Patric Bonnier , Harald Oberhauser

Although generative models have made remarkable progress in recent years, their use in critical applications has been hindered by an inability to reliably evaluate the quality of their generated samples. Quality refers to at least two…

Machine Learning · Computer Science 2026-02-18 Nicolas Salvy , Hugues Talbot , Bertrand Thirion

Diffusion models now generate high-quality, diverse samples, with an increasing focus on more powerful models. Although ensembling is a well-known way to improve supervised models, its application to unconditional score-based diffusion…

Machine Learning · Computer Science 2026-01-22 Raphaël Razafindralambo , Rémy Sun , Frédéric Precioso , Damien Garreau , Pierre-Alexandre Mattei

Deep generative models are powerful tools that have produced impressive results in recent years. These advances have been for the most part empirically driven, making it essential that we use high quality evaluation metrics. In this paper,…

Machine Learning · Statistics 2018-06-22 Shane Barratt , Rishi Sharma

Score-based Generative Models (SGMs) is one leading method in generative modeling, renowned for their ability to generate high-quality samples from complex, high-dimensional data distributions. The method enjoys empirical success and is…

Machine Learning · Computer Science 2024-01-30 Sixu Li , Shi Chen , Qin Li

In this work, we investigated the application of score-based gradient learning in discriminative and generative classification settings. Score function can be used to characterize data distribution as an alternative to density. It can be…

Machine Learning · Computer Science 2022-07-25 Yongchao Huang

Considering the difficulty of interpreting generative model output, there is significant current research focused on determining meaningful evaluation metrics. Several recent approaches utilize "precision" and "recall," borrowed from the…

Machine Learning · Computer Science 2025-02-28 Alexis Fox , Samarth Swarup , Abhijin Adiga

Generative models are a promising tool to produce cosmological simulations but face significant challenges in scalability, physical consistency, and adherence to domain symmetries, limiting their utility as alternatives to $N$-body…

Cosmology and Nongalactic Astrophysics · Physics 2025-08-26 Diana-Alexandra Onutu , Yue Zhao , Joaquin Vanschoren , Vlado Menkovski

Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include…

Machine Learning · Statistics 2018-04-27 Yingzhen Li , Richard E. Turner

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of…

Machine Learning · Statistics 2024-06-10 Aaron Lou , Chenlin Meng , Stefano Ermon

Policy targets evolve faster than the Coupled Model Intercomparison Project cycles, complicating adaptation and mitigation planning that must often contend with outdated projections. Climate model output emulators address this gap by…

Atmospheric and Oceanic Physics · Physics 2026-04-14 Shahine Bouabid , Andre Nogueira Souza , Raffaele Ferrari

We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on…

Machine Learning · Computer Science 2020-10-13 Yang Song , Stefano Ermon

To protect his teaching evaluations, an economics professor uses the following exam curve: if the class average falls below a known target, $m$, then all students will receive an equal number of free points so as to bring the mean up to…

Theoretical Economics · Economics 2021-08-13 Alex Garivaltis

Score-based generative models can produce high quality image samples comparable to GANs, without requiring adversarial optimization. However, existing training procedures are limited to images of low resolution (typically below 32x32), and…

Machine Learning · Computer Science 2020-10-27 Yang Song , Stefano Ermon

Devising indicative evaluation metrics for the image generation task remains an open problem. The most widely used metric for measuring the similarity between real and generated images has been the Fr\'echet Inception Distance (FID) score.…

Computer Vision and Pattern Recognition · Computer Science 2020-06-30 Muhammad Ferjad Naeem , Seong Joon Oh , Youngjung Uh , Yunjey Choi , Jaejun Yoo

The recent results of the BICEP and Keck collaborations have put stringent bounds on many inflationary models, including some well-motivated ones. This is certainly the case when gravity remains described by Einstein's theory up to the…

Cosmology and Nongalactic Astrophysics · Physics 2022-09-12 Alberto Salvio

We describe a probabilistic (generative) view of affinity matrices along with inference algorithms for a subclass of problems associated with data clustering. This probabilistic view is helpful in understanding different models and…

Machine Learning · Computer Science 2012-12-12 Romer Rosales , Brendan J. Frey

Recent advances in generative modeling have led to an increased interest in the study of statistical divergences as means of model comparison. Commonly used evaluation methods, such as the Frechet Inception Distance (FID), correlate well…

Machine Learning · Statistics 2018-10-30 Mehdi S. M. Sajjadi , Olivier Bachem , Mario Lucic , Olivier Bousquet , Sylvain Gelly

The evidence lower bound (ELBO) is one of the most central objectives for probabilistic unsupervised learning. For the ELBOs of several generative models and model classes, we here prove convergence to entropy sums. As one result, we…

Machine Learning · Statistics 2025-01-17 Jan Warnken , Dmytro Velychko , Simon Damm , Asja Fischer , Jörg Lücke
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