相关论文: Constraining Variational Inference with Geometric …

We consider linear inverse problems under white noise. These types of problems can be tackled with, e.g., iterative regularisation methods and the main challenge is to determine a suitable stopping index for the iteration. Convergence…

Matched filtering for signal detection in noisy data requires template banks that capture variation in signal waveforms while minimizing computational cost. Dimensionality reduction of signal waveforms can be important for building…

We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized Gaussian distribution. This…

Variational autoencoders (VAEs), one of the most widely used generative models, are known to suffer from posterior collapse, a phenomenon that reduces the diversity of generated samples. To avoid posterior collapse, many prior works have…

Most visual generative models compress images into a latent space before applying diffusion or autoregressive modelling. Yet, existing approaches such as VAEs and foundation model aligned encoders implicitly constrain the latent space…

Discrete latent bottlenecks in variational autoencoders (VAEs) offer high bit efficiency and can be modeled with autoregressive discrete distributions, enabling parameter-efficient multimodal search with transformers. However, discrete…

This paper discusses basic results and recent developments on variational regularization methods, as developed for inverse problems. In a typical setup we review basic properties needed to obtain a convergent regularization scheme and…

Generative Adversarial Networks (GANs) have significantly advanced image synthesis through mapping randomly sampled latent codes to high-fidelity synthesized images. However, applying well-trained GANs to real image editing remains…

Unsupervised learning-based anomaly detection in latent space has gained importance since discriminating anomalies from normal data becomes difficult in high-dimensional space. Both density estimation and distance-based methods to detect…

Lavrent'ev regularization for the autoconvolution equation was considered by J. Janno in {\itshape Lavrent'ev regularization of ill-posed problems containing nonlinear near-to-monotone operators with application to autoconvolution…

This work describes a novel data-driven latent space inference framework built on paired autoencoders to handle observational inconsistencies when solving inverse problems. Our approach uses two autoencoders, one for the parameter space and…

Our examination of existing deep generative models (DGMs), including VAEs and GANs, reveals two problems. First, their capability in handling discrete observations and latent codes is unsatisfactory, though there are interesting efforts.…

Selective manipulation of data attributes using deep generative models is an active area of research. In this paper, we present a novel method to structure the latent space of a Variational Auto-Encoder (VAE) to encode different…

We consider the variational reconstruction framework for inverse problems and propose to learn a data-adaptive input-convex neural network (ICNN) as the regularization functional. The ICNN-based convex regularizer is trained adversarially…

The ability to accurately model random fields plays a critical role in science and engineering for problems involving uncertain, spatially-varying quantities such as heterogeneous material properties and turbulent flows. Deep generative…

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view. We argue that vanilla VAE models unveil naturally a Riemannian structure in their latent space and that taking…

In disentangled representation learning, a model is asked to tease apart a dataset's underlying sources of variation and represent them independently of one another. Since the model is provided with no ground truth information about these…

One of the key challenges in learning joint embeddings of multiple modalities, e.g. of images and text, is to ensure coherent cross-modal semantics that generalize across datasets. We propose to address this through joint Gaussian…

Latent diffusion models have emerged as the leading approach for generating high-quality images and videos, utilizing compressed latent representations to reduce the computational burden of the diffusion process. While recent advancements…