Ignacio Peis

We introduce a novel generative framework for functions by integrating Implicit Neural Representations (INRs) and Transformer-based hypernetworks into latent variable models. Unlike prior approaches that rely on MLP-based hypernetworks with scalability limitations, our method employs a Transformer-based decoder to generate INR parameters from latent variables, addressing both representation capacity and computational efficiency. Our framework extends latent diffusion models (LDMs) to INR generation by replacing standard decoders with a Transformer-based hypernetwork, which can be trained either from scratch or via hyper-transforming: a strategy that fine-tunes only the decoder while freezing the pre-trained latent space. This enables efficient adaptation of existing generative models to INR-based representations without requiring full retraining. We validate our approach across multiple modalities, demonstrating improved scalability, expressiveness, and generalization over existing INR-based generative models. Our findings establish a unified and flexible framework for learning structured function representations.

Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally intensive when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VAMoH. VAMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VAMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VAMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VAMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.

Variational Autoencoders (VAEs) have recently been highly successful at imputing and acquiring heterogeneous missing data. However, within this specific application domain, existing VAE methods are restricted by using only one layer of latent variables and strictly Gaussian posterior approximations. To address these limitations, we present HH-VAEM, a Hierarchical VAE model for mixed-type incomplete data that uses Hamiltonian Monte Carlo with automatic hyper-parameter tuning for improved approximate inference. Our experiments show that HH-VAEM outperforms existing baselines in the tasks of missing data imputation and supervised learning with missing features. Finally, we also present a sampling-based approach for efficiently computing the information gain when missing features are to be acquired with HH-VAEM. Our experiments show that this sampling-based approach is superior to alternatives based on Gaussian approximations.