While deep neural networks possess the capability to perform semantic segmentation, producing a single deterministic output limits reliability in safety-critical applications caused by uncertainty and annotation variability. To address this, stochastic segmentation models using Conditional Variational Autoencoders (CVAE), Bayesian networks, and diffusion have been explored. However, existing approaches suffer from limited latent expressiveness and interpretability. Furthermore, our experiments showed that models like Probabilistic U-Net rely excessively on high latent variance, leading to posterior collapse. This work propose a novel framework by integrating Gaussian Mixture Model (GMM) with Normalizing Flow (NF) in CVAE for stochastic segmentation. GMM structures the latent space into meaningful semantic clusters, while NF captures feature deformations with quantified uncertainty. Our method stabilizes latent distributions through constrained variance and mean ranges. Experiments on LIDC, Crack500, and Cityscapes datasets show that our approach outperformed state-of-the-art in curvilinear structure and medical image segmentation.

Diffusion bridge models and stochastic interpolants enable high-quality imageto-image (I2I) translation by creating paths between distributions in pixel space. However, recent diffusion bridge models excel in image translation but suffer from restricted design flexibility and complicated hyperparameter tuning, whereas Stochastic Interpolants offer greater flexibility but lack essential refinements. We show that these complementary strengths can be unified by interpreting all existing methods within a single SI-based framework. In this work, we unify and expand the space of bridge models by extending Stochastic Interpolants (SIs) with preconditioning, endpoint conditioning, and an optimized sampling algorithm. These enhancements expand the design space of diffusion bridge models, leading to state-of-the-art performance in both image quality and sampling efficiency across diverse I2I tasks. Furthermore, we identify and address a previously overlooked issue of low sample diversity under fixed conditions. We introduce a quantitative analysis for output diversity and demonstrate how we can modify the base distribution for further improvements. Code is available at https://github.com/szhan311/ECSI.

Density estimation and reliable prediction regions for outputs are crucial in supervised and unsupervised learning. While conformal prediction effectively generates coverage-guaranteed regions, it struggles with multi-dimensional outputs due to reliance on one-dimensional nonconformity scores. To address this, we introduce CONTRA: CONformal prediction region via normalizing flow TRAnsformation. CONTRA utilizes the latent spaces of normalizing flows to define nonconformity scores based on distances from the center. This allows for the mapping of high-density regions in latent space to sharp prediction regions in the output space, surpassing traditional hyperrectangular or elliptical conformal regions. Further, for scenarios where other predictive models are favored over flow-based models, we extend CONTRA to enhance any such model with a reliable prediction region by training a simple normalizing flow on the residuals. We demonstrate that both CONTRA and its extension maintain guaranteed coverage probability and outperform existing methods in generating accurate prediction regions across various datasets. We conclude that CONTRA is an effective tool for (conditional) density estimation, addressing the under-explored challenge of delivering multi-dimensional prediction regions.

However, previous NF-based methods forcibly transform the distribution of all features into a single distribution (e.g., unit normal distribution), even when the features can have locally distinct semantic information and thus follow different

We study how tail properties of the base distribution of a NEF impose limits on the NEF: if the base distribution is subexponential (subgaussian), we show that the NEF is self-concordant with a stretch factor that grows inverse quadratically (respectively, linearly) 2.

Material discovery holds transformative potential across numerous industries including carbon capture[38], batteries[28], photovoltaics[9], and energy storage[1]. LLMs excel atmodeling discrete values, but they can struggle with continuous values due to their reliance on finite precision representations.

Graph generative modelling has become an essential task due to the wide range of applications in chemistry, biology, social networks, and knowledge representation. In this work, we propose a novel framework for generating graphs by adapting the Generator Matching (arXiv:2410.20587) paradigm to graph-structured data. We leverage the graph Laplacian and its associated heat kernel to define a continous-time diffusion on each graph. The Laplacian serves as the infinitesimal generator of this diffusion, and its heat kernel provides a family of conditional perturbations of the initial graph. A neural network is trained to match this generator by minimising a Bregman divergence between the true generator and a learnable surrogate. Once trained, the surrogate generator is used to simulate a time-reversed diffusion process to sample new graph structures. Our framework unifies and generalises existing diffusion-based graph generative models, injecting domain-specific inductive bias via the Laplacian, while retaining the flexibility of neural approximators. Experimental studies demonstrate that our approach captures structural properties of real and synthetic graphs effectively.