Inverting Data Transformations via Diffusion Sampling

• URL: http://arxiv.org/abs/2602.08267v1
• Date: Mon, 09 Feb 2026 04:58:34 GMT
• Title: Inverting Data Transformations via Diffusion Sampling
• Authors: Jinwoo Kim, Sékou-Oumar Kaba, Jiyun Park, Seunghoon Hong, Siamak Ravanbakhsh,
• Abstract summary: We study the problem of transformation inversion on general Lie groups.<n>The goal is to recover an inverse transformation that maps it back to the original data distribution.<n>We take a probabilistic view and model the posterior over transformations as a Boltzmann distribution.
• Score: 33.6473603169954
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the problem of transformation inversion on general Lie groups: a datum is transformed by an unknown group element, and the goal is to recover an inverse transformation that maps it back to the original data distribution. Such unknown transformations arise widely in machine learning and scientific modeling, where they can significantly distort observations. We take a probabilistic view and model the posterior over transformations as a Boltzmann distribution defined by an energy function on data space. To sample from this posterior, we introduce a diffusion process on Lie groups that keeps all updates on-manifold and only requires computations in the associated Lie algebra. Our method, Transformation-Inverting Energy Diffusion (TIED), relies on a new trivialized target-score identity that enables efficient score-based sampling of the transformation posterior. As a key application, we focus on test-time equivariance, where the objective is to improve the robustness of pretrained neural networks to input transformations. Experiments on image homographies and PDE symmetries demonstrate that TIED can restore transformed inputs to the training distribution at test time, showing improved performance over strong canonicalization and sampling baselines. Code is available at https://github.com/jw9730/tied.

Related papers

• EquiReg: Equivariance Regularized Diffusion for Inverse Problems [67.01847869495558]
  We propose EquiReg diffusion, a framework for regularizing posterior sampling in diffusion-based inverse problem solvers.<n>When applied to a variety of solvers, EquiReg outperforms state-of-the-art diffusion models in both linear and nonlinear image restoration tasks.
  arXiv  Detail & Related papers  (2025-05-29T01:25:43Z)
• Unsupervised Representation Learning from Sparse Transformation Analysis [79.94858534887801]
  We propose to learn representations from sequence data by factorizing the transformations of the latent variables into sparse components. Input data are first encoded as distributions of latent activations and subsequently transformed using a probability flow model.
  arXiv  Detail & Related papers  (2024-10-07T23:53:25Z)
• Perturbative partial moment matching and gradient-flow adaptive importance sampling transformations for Bayesian leave one out cross-validation [0.9895793818721335]
  We motivate the use of perturbative transformations of the form $T(boldsymboltheta)=boldsymboltheta + h Q(boldsymboltheta),$ for $0hll 1,$.<n>We derive closed-form expressions in the case of logistic regression and shallow ReLU activated neural networks.
  arXiv  Detail & Related papers  (2024-02-13T01:03:39Z)
• Learning Collective Variables with Synthetic Data Augmentation through Physics-Inspired Geodesic Interpolation [1.4972659820929493]
  In molecular dynamics simulations, rare events, such as protein folding, are typically studied using enhanced sampling techniques. We propose a simulation-free data augmentation strategy using physics-inspired metrics to generate geodesics resembling protein folding transitions.
  arXiv  Detail & Related papers  (2024-02-02T16:35:02Z)
• Equivariance Discovery by Learned Parameter-Sharing [153.41877129746223]
  We study how to discover interpretable equivariances from data. Specifically, we formulate this discovery process as an optimization problem over a model's parameter-sharing schemes. Also, we theoretically analyze the method for Gaussian data and provide a bound on the mean squared gap between the studied discovery scheme and the oracle scheme.
  arXiv  Detail & Related papers  (2022-04-07T17:59:19Z)
• Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration [77.99182201815763]
  Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. We propose a novel monomial selection algorithm based on pruning methods to allow an application to more complex problems. We demonstrate the improved sample complexity on the Rotated-MNIST, SVHN and CIFAR-10 datasets.
  arXiv  Detail & Related papers  (2022-02-08T16:16:11Z)
• Revisiting Transformation Invariant Geometric Deep Learning: An Initial Representation Perspective [38.314914702299056]
  We propose Transformation In Neural Networks (TinvNN), a straightforward and general plug-in for geometric data.<n>Specifically, we realize transformation invariant and distance-preserving initial point representations by modifying multi-dimensional scaling.<n>We prove that TinvNN can strictly guarantee transformation invariant, being general and flexible enough to be combined with the existing neural networks.
  arXiv  Detail & Related papers  (2021-12-23T03:52:33Z)
• Quantised Transforming Auto-Encoders: Achieving Equivariance to Arbitrary Transformations in Deep Networks [23.673155102696338]
  Convolutional Neural Networks (CNNs) are equivariant to image translation. We propose an auto-encoder architecture whose embedding obeys an arbitrary set of equivariance relations simultaneously. We demonstrate results of successful re-rendering of transformed versions of input images on several datasets.
  arXiv  Detail & Related papers  (2021-11-25T02:26:38Z)
• Topographic VAEs learn Equivariant Capsules [84.33745072274942]
  We introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. We demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks.
  arXiv  Detail & Related papers  (2021-09-03T09:25:57Z)
• Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data [52.78581260260455]
  We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group. We apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems.
  arXiv  Detail & Related papers  (2020-02-25T17:40:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.