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Jae Hyun Lim

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3 papers

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JMLR Journal 2025 Journal Article

Score-Based Diffusion Models in Function Space

Jae Hyun Lim
Nikola B. Kovachki
Ricardo Baptista
Christopher Beckham
Kamyar Azizzadenesheli
Jean Kossaifi
Vikram Voleti
Jiaming Song

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising. Despite their tremendous success, they are mostly formulated on finite-dimensional spaces, e.g., Euclidean, limiting their applications to many domains where the data has a functional form, such as in scientific computing and 3D geometric data analysis. This work introduces a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. In DDOs, the forward process perturbs input functions gradually using a Gaussian process. The generative process is formulated by a function-valued annealed Langevin dynamic. Our approach requires an appropriate notion of the score for the perturbed data distribution, which we obtain by generalizing denoising score matching to function spaces that can be infinite-dimensional. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution. We theoretically and numerically verify the applicability of our approach on a set of function-valued problems, including generating solutions to the Navier-Stokes equation viewed as the push-forward distribution of forcings from a Gaussian Random Field (GRF), as well as volcano InSAR and MNIST-SDF. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2025. ( edit, beta )

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NeurIPS Conference 2021 Conference Paper

A Variational Perspective on Diffusion-Based Generative Models and Score Matching

Chin-Wei Huang
Jae Hyun Lim
Aaron C. Courville

Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can be reversed via learning the score function, i. e. the gradient of the log-density of the perturbed data. They propose to plug the learned score function into an inverse formula to define a generative diffusion process. Despite the empirical success, a theoretical underpinning of this procedure is still lacking. In this work, we approach the (continuous-time) generative diffusion directly and derive a variational framework for likelihood estimation, which includes continuous-time normalizing flows as a special case, and can be seen as an infinitely deep variational autoencoder. Under this framework, we show that minimizing the score-matching loss is equivalent to maximizing a lower bound of the likelihood of the plug-in reverse SDE proposed by Song et al. (2021), bridging the theoretical gap.

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NeurIPS Conference 2019 Conference Paper

Neural Multisensory Scene Inference

Jae Hyun Lim
Pedro O. Pinheiro
Negar Rostamzadeh
Chris Pal
Sungjin Ahn

For embodied agents to infer representations of the underlying 3D physical world they inhabit, they should efficiently combine multisensory cues from numerous trials, e. g. , by looking at and touching objects. Despite its importance, multisensory 3D scene representation learning has received less attention compared to the unimodal setting. In this paper, we propose the Generative Multisensory Network (GMN) for learning latent representations of 3D scenes which are partially observable through multiple sensory modalities. We also introduce a novel method, called the Amortized Product-of-Experts, to improve the computational efficiency and the robustness to unseen combinations of modalities at test time. Experimental results demonstrate that the proposed model can efficiently infer robust modality-invariant 3D-scene representations from arbitrary combinations of modalities and perform accurate cross-modal generation. To perform this exploration we have also developed a novel multi-sensory simulation environment for embodied agents.

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