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1. Diffusion Models With Learned Adaptive Noise

   Sahoo, Subham; Gokaslan, Aaron; De_Sa, Christopher; Kuleshov, Volodymyr (December 2024, NeurIPS 2024)

   Diffusion models have gained traction as powerful algorithms for synthesizing high-quality images. Central to these algorithms is the diffusion process, a set of equations which maps data to noise in a way that can significantly affect performance. In this paper, we explore whether the diffusionprocess can be learned from data.Our work is grounded in Bayesian inference and seeks to improve log-likelihood estimation by casting the learned diffusion process as an approximate variational posterior that yields a tighter lower bound (ELBO) on the likelihood.A widely held assumption is that the ELBO is invariant to the noise process: our work dispels this assumption and proposes multivariate learned adaptive noise (MuLAN), a learned diffusion process that applies noise at different rates across an image. Our method consists of three components: a multivariate noise schedule, adaptive input-conditional diffusion, and auxiliary variables; these components ensure that the ELBO is no longer invariant to the choice of the noise schedule as in previous works. Empirically, MuLAN sets a new state-of-the-art in density estimation on CIFAR-10 and ImageNet while matching the performance of previous state-of-the-art models with 50% fewer steps. We provide the code, along with a blog post and video tutorial on the project page: https://s-sahoo.com/MuLAN 

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2. Boomerang: Local Sampling on Image Manifolds using Diffusion Models

   Luzi, L; Siahkoohi, A; Mayer, P M; Casco-Rodriguez, J; Baraniuk, R G (November 2023, Transactions on machine learning research)

   The inference stage of diffusion models involves running a reverse-time diffusion stochastic differential equation, transforming samples from a Gaussian latent distribution into samples from a target distribution on a low-dimensional manifold. The intermediate values can be interpreted as noisy images, with the amount of noise determined by the forward diffusion process noise schedule. Boomerang is an approach for local sampling of image manifolds, which involves adding noise to an input image, moving it closer to the latent space, and mapping it back to the image manifold through a partial reverse diffusion process. Boomerang can be used with any pretrained diffusion model without adjustments to the reverse diffusion process, and we present three applications: constructing privacy-preserving datasets with controllable anonymity, increasing generalization performance with Boomerang for data augmentation, and enhancing resolution with a perceptual image enhancement framework. 

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3. Spatial factor modeling: A Bayesian matrix‐normal approach for misaligned data

   https://doi.org/10.1111/biom.13452  

   Zhang, Lu; Banerjee, Sudipto (March 2021, Biometrics)

   Abstract Multivariate spatially oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for each variable and associations among the different dependent variables. Multivariate latent spatial process models have proved effective in driving statistical inference and rendering better predictive inference at arbitrary locations for the spatial process. High‐dimensional multivariate spatial data, which are the theme of this article, refer to data sets where the number of spatial locations and the number of spatially dependent variables is very large. The field has witnessed substantial developments in scalable models for univariate spatial processes, but such methods for multivariate spatial processes, especially when the number of outcomes are moderately large, are limited in comparison. Here, we extend scalable modeling strategies for a single process to multivariate processes. We pursue Bayesian inference, which is attractive for full uncertainty quantification of the latent spatial process. Our approach exploits distribution theory for the matrix‐normal distribution, which we use to construct scalable versions of a hierarchical linear model of coregionalization (LMC) and spatial factor models that deliver inference over a high‐dimensional parameter space including the latent spatial process. We illustrate the computational and inferential benefits of our algorithms over competing methods using simulation studies and an analysis of a massive vegetation index data set. 

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4. Diffusion-HMC: Parameter Inference with Diffusion-model-driven Hamiltonian Monte Carlo

   https://doi.org/10.3847/1538-4357/ad8bc3  

   Mudur, Nayantara; Cuesta-Lazaro, Carolina; Finkbeiner, Douglas_P (December 2024, The Astrophysical Journal)

   Abstract Diffusion generative models have excelled at diverse image generation and reconstruction tasks across fields. A less explored avenue is their application to discriminative tasks involving regression or classification problems. The cornerstone of modern cosmology is the ability to generate predictions for observed astrophysical fields from theory and constrain physical models from observations using these predictions. This work uses a single diffusion generative model to address these interlinked objectives—as a surrogate model or emulator for cold dark matter density fields conditional on input cosmological parameters, and as a parameter inference model that solves the inverse problem of constraining the cosmological parameters of an input field. The model is able to emulate fields with summary statistics consistent with those of the simulated target distribution. We then leverage the approximate likelihood of the diffusion generative model to derive tight constraints on cosmology by using the Hamiltonian Monte Carlo method to sample the posterior on cosmological parameters for a given test image. Finally, we demonstrate that this parameter inference approach is more robust to small perturbations of noise to the field than baseline parameter inference networks. 

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5. Causal Diffusion Autoencoders: Toward Counterfactual Generation via Diffusion Probabilistic Models

   https://doi.org/10.3233/FAIA240780  

   Komanduri, Aneesh; Zhao, Chen; Chen, Feng; Wu, Xintao (October 2024, IOS Press)

   Diffusion probabilistic models (DPMs) have become the state-of-the-art in high-quality image generation. However, DPMs have an arbitrary noisy latent space with no interpretable or controllable semantics. Although there has been significant research effort to improve image sample quality, there is little work on representation-controlled generation using diffusion models. Specifically, causal modeling and controllable counterfactual generation using DPMs is an underexplored area. In this work, we propose CausalDiffAE, a diffusion-based causal representation learning framework to enable counterfactual generation according to a specified causal model. Our key idea is to use an encoder to extract high-level semantically meaningful causal variables from high-dimensional data and model stochastic variation using reverse diffusion. We propose a causal encoding mechanism that maps high-dimensional data to causally related latent factors and parameterize the causal mechanisms among latent factors using neural networks. To enforce the disentanglement of causal variables, we formulate a variational objective and leverage auxiliary label information in a prior to regularize the latent space. We propose a DDIM-based counterfactual generation procedure subject to do-interventions. Finally, to address the limited label supervision scenario, we also study the application of CausalDiffAE when a part of the training data is unlabeled, which also enables granular control over the strength of interventions in generating counterfactuals during inference. We empirically show that CausalDiffAE learns a disentangled latent space and is capable of generating high-quality counterfactual images. 

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