Mayank Nautiyal

Mayank Nautiyal, Li Ju, Andreas Hellander et al.

Standard dual-encoder vision-language models that map images and text to deterministic points on a shared unit hypersphere through $\ell_2$ normalization typically expose neither \emph{aleatoric} uncertainty (cross-modal ambiguity) nor \emph{epistemic} uncertainty (lack of training-distribution support). Existing post-hoc methods either recover at most one of the two uncertainty components, or ignore the hyperspherical geometry of these models' embeddings. We propose \textbf{GeoFlowVLM} as a post-hoc adapter that learns the joint distribution of paired $\ell_2$-normalised dual-encoder VLM embeddings on the product hypersphere $\mathbb{S}^{d-1} \times \mathbb{S}^{d-1}$ via Riemannian flow matching with a single masked velocity field. A consistency result shows that, in the population limit, the trained network exposes the joint flow and both cross-modal conditional flows as valid Riemannian flow-matching velocity fields on their respective domains. We derive two quantities from this single model: a conditional retrieval entropy that quantifies aleatoric ambiguity with a decision-theoretic interpretation via a Fano-type bound, and a marginal-typicality epistemic score justified by an exact chain-rule decomposition of the joint NLL. This decomposition isolates a cross-modal pointwise-mutual-information term that is structurally discriminative rather than epistemic, and is empirically the only consistently uninformative standalone component. Empirically, the entropy tracks Recall@1 with near-ideal monotonic calibration across three retrieval benchmarks in both directions, and the marginal-typicality sum yields consistently calibrated selective accuracy across four zero-shot classification benchmarks.

Li Ju, Mayank Nautiyal, Andreas Hellander et al.

Vision-Language Models (VLMs) are typically deterministic in nature and lack intrinsic mechanisms to quantify epistemic uncertainty, which reflects the model's lack of knowledge or ignorance of its own representations. We theoretically motivate negative log-density of an embedding as a proxy for the epistemic uncertainty, where low-density regions signify model ignorance. The proposed method REPVLM computes the probability density on the hyperspherical manifold of the VLM embeddings using Riemannian Flow Matching. We empirically demonstrate that REPVLM achieves near-perfect correlation between uncertainty and prediction error, significantly outperforming existing baselines. Beyond classification, we also demonstrate that the model also provides a scalable metric for out-of-distribution detection and automated data curation.

Mayank Nautiyal, Li Ju, Melker Ernfors et al.

We introduce \textit{OneFlowSBI}, a unified framework for simulation-based inference that learns a single flow-matching generative model over the joint distribution of parameters and observations. Leveraging a query-aware masking distribution during training, the same model supports multiple inference tasks, including posterior sampling, likelihood estimation, and arbitrary conditional distributions, without task-specific retraining. We evaluate \textit{OneFlowSBI} on ten benchmark inference problems and two high-dimensional real-world inverse problems across multiple simulation budgets. \textit{OneFlowSBI} is shown to deliver competitive performance against state-of-the-art generalized inference solvers and specialized posterior estimators, while enabling efficient sampling with few ODE integration steps and remaining robust under noisy and partially observed data.

Mayank Nautiyal, Andrey Shternshis, Andreas Hellander et al.

We present a generative modeling approach based on the variational inference framework for likelihood-free simulation-based inference. The method leverages latent variables within variational autoencoders to efficiently estimate complex posterior distributions arising from stochastic simulations. We explore two variations of this approach distinguished by their treatment of the prior distribution. The first model adapts the prior based on observed data using a multivariate prior network, enhancing generalization across various posterior queries. In contrast, the second model utilizes a standard Gaussian prior, offering simplicity while still effectively capturing complex posterior distributions. We demonstrate the ability of the proposed approach to approximate complex posteriors while maintaining computational efficiency on well-established benchmark problems.

Mayank Nautiyal, Andreas Hellander, Prashant Singh

We present a conditional diffusion model - ConDiSim, for simulation-based inference of complex systems with intractable likelihoods. ConDiSim leverages denoising diffusion probabilistic models to approximate posterior distributions, consisting of a forward process that adds Gaussian noise to parameters, and a reverse process learning to denoise, conditioned on observed data. This approach effectively captures complex dependencies and multi-modalities within posteriors. ConDiSim is evaluated across ten benchmark problems and two real-world test problems, where it demonstrates effective posterior approximation accuracy while maintaining computational efficiency and stability in model training. ConDiSim offers a robust and extensible framework for simulation-based inference, particularly suitable for parameter inference workflows requiring fast inference methods.

Mayank Nautiyal, Stela Arranz Gheorghe, Kristiana Stefa et al.

Language-guided attention frameworks have significantly enhanced both interpretability and performance in image classification; however, the reliance on deterministic embeddings from pre-trained vision-language foundation models to generate reference attention maps frequently overlooks the intrinsic multivaluedness and ill-posed characteristics of cross-modal mappings. To address these limitations, we introduce PARIC, a probabilistic framework for guiding visual attention via language specifications. Our approach enables pre-trained vision-language models to generate probabilistic reference attention maps, which align textual and visual modalities more effectively while incorporating uncertainty estimates, as compared to their deterministic counterparts. Experiments on benchmark test problems demonstrate that PARIC enhances prediction accuracy, mitigates bias, ensures consistent predictions, and improves robustness across various datasets.