The rapid progress of diffusion models highlights the growing need for detecting generated images. Previous research demonstrates that incorporating diffusion-based measurements, such as reconstruction error, can enhance the gener-alizability of detectors. However, ignoring the differing impacts of aleatoric and epistemic uncertainty on reconstruction error can undermine detection performance. Aleatoric uncertainty, arising from inherent data noise, creates ambiguity that impedes accurate detection of generated images. As it reflects random variations within the data (e.g., noise in natural textures), it does not help distinguish generated images. In contrast, epistemic uncertainty, which represents the model's lack of knowledge about unfamiliar patterns, supports detection. In this paper, we propose a novel framework, Diffusion Epistemic Uncertainty with Asymmetric Learning (DEUA), for detecting diffusion-generated images. W e introduce Diffusion Epistemic Uncertainty (DEU) estimation via the Laplace approximation to assess the proximity of data to the manifold of diffusion-generated samples. Additionally, an asymmetric loss function is introduced to train a balanced classifier with larger margins, further enhancing generalizability.

We develop a multilevel Monte Carlo (MLMC) framework for uncertainty quantification with Monte Carlo dropout. Treating dropout masks as a source of epistemic randomness, we define a fidelity hierarchy by the number of stochastic forward passes used to estimate predictive moments. We construct coupled coarse--fine estimators by reusing dropout masks across fidelities, yielding telescoping MLMC estimators for both predictive means and predictive variances that remain unbiased for the corresponding dropout-induced quantities while reducing sampling variance at fixed evaluation budget. We derive explicit bias, variance and effective cost expressions, together with sample-allocation rules across levels. Numerical experiments on forward and inverse PINNs--Uzawa benchmarks confirm the predicted variance rates and demonstrate efficiency gains over single-level MC-dropout at matched cost.

A probabilistic formulation of irreversible kinetics is introduced in which incrementally admissible histories are weighted by a Gibbs-type measure built from an energy-dissipation action and observation constraints, with Theta controlling epistemic uncertainty. This measure can be interpreted as a Bayesian posterior over histories. In the zero-uncertainty limit, it concentrates on maximum-a-posteriori (MAP) histories, recovering classical deterministic evolution by incremental minimization in the convex generalized-standard-material setting, while allowing multiple competing MAP histories for non-convex energies or temporally coupled constraints. This emergence is demonstrated across seven distinct forward-in-time examples and an inverse inference problem of unknown histories from sparse observations via a global constrained minimum-action principle.

Offline reinforcement learning (RL) is suitable for safety-critical domains where online exploration is not feasible. In such domains, decision-making should take into consideration the risk of catastrophic outcomes. In other words, decision-making should be . An additional challenge of offline RL is avoiding, i.e. ensuring that state-action pairs visited by the policy remain near those in the dataset. Previous offline RL algorithms that consider risk combine offline RL techniques (to avoid distributional shift), with risk-sensitive RL algorithms (to achieve risk-aversion).

Flexibly quantifying both irreducible aleatoric and model-dependent epistemic uncertainties plays an important role for complex regression problems. While deep neural networks in principle can provide this flexibility and learn heteroscedastic aleatoric uncertainties through non-linear functions, recent works highlight that maximizing the log likelihood objective parameterized by mean and variance can lead to compromised mean fits since the gradient are scaled by the predictive variance, and propose adjustments in line with this premise. We instead propose to use the natural parametrization of the Gaussian, which has been shown to be more stable for heteroscedastic regression based on non-linear feature maps and Gaussian processes. Further, we emphasize the significance of principled regularization of the network parameters and prediction. We therefore propose an efficient Laplace approximation for heteroscedastic neural networks that allows automatic regularization through empirical Bayes and provides epistemic uncertainties, both of which improve generalization.We showcase on a range of regression problems--including a new heteroscedastic image regression benchmark--that our methods are scalable, improve over previous approaches for heteroscedastic regression, and provide epistemic uncertainty without requiring hyperparameter tuning.

We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single-and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.