Generative Uncertainty in Diffusion Models

Diffusion models have recently driven significant breakthroughs in generative modeling. While state-of-the-art models produce high-quality samples on average, individual samples can still be low quality. Detecting such samples without human inspection remains a challenging task. To address this, we propose a Bayesian framework for estimating generative uncertainty of synthetic samples. We outline how to make Bayesian inference practical for large, modern generative models and introduce a new semantic likelihood (evaluated in the latent space of a feature extractor) to address the challenges posed by high-dimensional sample spaces. Through our experiments, we demonstrate that the proposed generative uncertainty effectively identifies poor-quality samples and significantly outperforms existing uncertainty-based methods. Notably, our Bayesian framework can be applied post-hoc to any pretrained diffusion or flow matching model (via the Laplace approximation), and we propose simple yet effective techniques to minimize its computational overhead during sampling.

JANET: Joint Adaptive predictioN-region Estimation for Time-series

Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET's superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.

Understanding Pathologies of Deep Heteroskedastic Regression

Several recent studies have reported negative results when using heteroskedastic neural regression models to model real-world data. In particular, for overparameterized models, the mean and variance networks are powerful enough to either fit every single data point (while shrinking the predicted variances to zero), or to learn a constant prediction with an output variance exactly matching every predicted residual (i.e., explaining the targets as pure noise). This paper studies these difficulties from the perspective of statistical physics. We show that the observed instabilities are not specific to any neural network architecture but are already present in a field theory of an overparameterized conditional Gaussian likelihood model. Under light assumptions, we derive a nonparametric free energy that can be solved numerically. The resulting solutions show excellent qualitative agreement with empirical model fits on real-world data and, in particular, prove the existence of phase transitions, i.e., abrupt, qualitative differences in the behaviors of the regressors upon varying the regularization strengths on the two networks. Our work thus provides a theoretical explanation for the necessity to carefully regularize heteroskedastic regression models. Moreover, the insights from our theory suggest a scheme for optimizing this regularization which is quadratically more efficient than the naive approach.