FrePolad: Frequency-Rectified Point Latent Diffusion for Point Cloud Generation

We propose FrePolad: frequency-rectified point latent diffusion, a point cloud generation pipeline integrating a variational autoencoder (VAE) with a denoising diffusion probabilistic model (DDPM) for the latent distribution. FrePolad simultaneously achieves high quality, diversity, and flexibility in point cloud cardinality for generation tasks while maintaining high computational efficiency. The improvement in generation quality and diversity is achieved through (1) a novel frequency rectification module via spherical harmonics designed to retain high-frequency content while learning the point cloud distribution; and (2) a latent DDPM to learn the regularized yet complex latent distribution. In addition, FrePolad supports variable point cloud cardinality by formulating the sampling of points as conditional distributions over a latent shape distribution. Finally, the low-dimensional latent space encoded by the VAE contributes to FrePolad's fast and scalable sampling. Our quantitative and qualitative results demonstrate the state-of-the-art performance of FrePolad in terms of quality, diversity, and computational efficiency.

Neural Fields with Hard Constraints of Arbitrary Differential Order

While deep learning techniques have become extremely popular for solving a broad range of optimization problems, methods to enforce hard constraints during optimization, particularly on deep neural networks, remain underdeveloped. Inspired by the rich literature on meshless interpolation and its extension to spectral collocation methods in scientific computing, we develop a series of approaches for enforcing hard constraints on neural fields, which we refer to as \emph{Constrained Neural Fields} (CNF). The constraints can be specified as a linear operator applied to the neural field and its derivatives. We also design specific model representations and training strategies for problems where standard models may encounter difficulties, such as conditioning of the system, memory consumption, and capacity of the network when being constrained. Our approaches are demonstrated in a wide range of real-world applications. Additionally, we develop a framework that enables highly efficient model and constraint specification, which can be readily applied to any downstream task where hard constraints need to be explicitly satisfied during optimization.

HyperTime: Implicit Neural Representation for Time Series

Implicit neural representations (INRs) have recently emerged as a powerful tool that provides an accurate and resolution-independent encoding of data. Their robustness as general approximators has been shown in a wide variety of data sources, with applications on image, sound, and 3D scene representation. However, little attention has been given to leveraging these architectures for the representation and analysis of time series data. In this paper, we analyze the representation of time series using INRs, comparing different activation functions in terms of reconstruction accuracy and training convergence speed. We show how these networks can be leveraged for the imputation of time series, with applications on both univariate and multivariate data. Finally, we propose a hypernetwork architecture that leverages INRs to learn a compressed latent representation of an entire time series dataset. We introduce an FFT-based loss to guide training so that all frequencies are preserved in the time series. We show that this network can be used to encode time series as INRs, and their embeddings can be interpolated to generate new time series from existing ones. We evaluate our generative method by using it for data augmentation, and show that it is competitive against current state-of-the-art approaches for augmentation of time series.

Neural BRDF Representation and Importance Sampling

Controlled capture of real-world material appearance yields tabulated sets of highly realistic reflectance data. In practice, however, its high memory footprint requires compressing into a representation that can be used efficiently in rendering while remaining faithful to the original. Previous works in appearance encoding often prioritised one of these requirements at the expense of the other, by either applying high-fidelity array compression strategies not suited for efficient queries during rendering, or by fitting a compact analytic model that lacks expressiveness. We present a compact neural network-based representation of BRDF data that combines high-accuracy reconstruction with efficient practical rendering via built-in interpolation of reflectance. We encode BRDFs as lightweight networks, and propose a training scheme with adaptive angular sampling, critical for the accurate reconstruction of specular highlights. Additionally, we propose a novel approach to make our representation amenable to importance sampling: rather than inverting the trained networks, we learn an embedding that can be mapped to parameters of an analytic BRDF for which importance sampling is known. We evaluate encoding results on isotropic and anisotropic BRDFs from multiple real-world datasets, and importance sampling performance for isotropic BRDFs mapped to two different analytic models.