DiffATS: Diffusion in Aligned Tensor Space

• URL: http://arxiv.org/abs/2605.09275v1
• Date: Sun, 10 May 2026 02:53:43 GMT
• Title: DiffATS: Diffusion in Aligned Tensor Space
• Abstract summary: We construct data-dependent tensor primitives without pretrained compression autoencoders.<n> *Diffusion in Space* (DiffATS) is a generative framework that trains diffusion models directly on tensor primitives.
• Score: 3.8961572818716768
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Direct diffusion modeling of high-resolution spatiotemporal fields is computationally challenging. Parameter-efficient primitives address this by representing high-dimensional data with a compact set of parameters. In this paper, we construct data-dependent tensor primitives without pretrained compression autoencoders. Our construction starts from Tucker decomposition, which captures low-rank multilinear structure through a core tensor and mode-wise factors. However, Tucker factors are non-unique: the same tensor can be represented by different rotated factors, which complicates generative modeling. We address this issue with orthogonal Procrustes (OP) alignment. Specifically, we select medoid anchor matrices from the data and align the factor matrices to resolve the gauge ambiguity. This yields matrix Grassmannian primitives and tensor Grassmannian primitives that are compact, data-adaptive, and directly decodable by explicit multilinear reconstruction. Theoretically, we prove that the proposed primitive maps are homeomorphisms between low-rank tensors and their corresponding primitive spaces, certifying that the representations are non-degenerate and topologically faithful. Building on these primitives, we propose *Diffusion in Aligned Tensor Space* (DiffATS), a generative framework that trains diffusion models directly on aligned tensor primitives. Across images, videos, and PDE solutions, DiffATS achieves strong unconditional and conditional generation performance while compressing original data by $3.9\times$ to $210\times$, without relying on any pretrained deep compression autoencoders.

Related papers

• Convolutional Symmetric AutoEncoders: enhancing latent stability via differential geometry [0.0]
  This study builds upon works by arXiv:2307.15288v2 and arXiv:2506.11641v1 by extending representation consistency for convolutional layers.<n>We introduce a novel class of symmetric Convolutional AutoEncoders (CAEs) designed to embody the primary properties of manifold parametrization mappings.
  arXiv  Detail & Related papers  (2026-07-01T09:16:37Z)
• Constructing VAE Latent Spaces with Prescribed Topology [5.207307163958805]
  Variational autoencoders learn low-dimensional latent representations of high-dimensional data.<n>Topology-aware models outperform the Gaussian baseline at all practically relevant regularization strengths.
  arXiv  Detail & Related papers  (2026-06-05T08:59:55Z)
• Rethinking Diffusion Models with Symmetries through Canonicalization with Applications to Molecular Graph Generation [56.361076943802594]
  CanonFlow achieves state-of-the-art performance on the challenging GEOM-DRUG dataset, and the advantage remains large in few-step generation.
  arXiv  Detail & Related papers  (2026-02-16T18:58:55Z)
• Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization [49.85875869048434]
  We propose a CP-based low-rank tensor function parameterized by neural networks for implicit neural representation.<n>To achieve sparser CP decomposition, we introduce a variational Schatten-p quasi-norm to prune redundant rank-1 components.<n>For smoothness, we propose a regularization term based on the spectral norm of the Jacobian and Hutchinson's trace estimator.
  arXiv  Detail & Related papers  (2025-06-27T11:23:10Z)
• Orientation-Aware Sparse Tensor PCA for Efficient Unsupervised Feature Selection [7.887782360541216]
  We introduce Decomposition (TD) techniques into unsupervised feature selection (UFS)<n>We use the orientation-dependent tensor-tensor product from sparse Singular Value Decomposition to solve the problem.<n>The proposed tensor PCA model can constrain sparsity at the specified mode and yield sparse tensor principal components.
  arXiv  Detail & Related papers  (2024-07-24T04:04:56Z)
• Efficient Nonparametric Tensor Decomposition for Binary and Count Data [27.02813234958821]
  We propose ENTED, an underlineEfficient underlineNon underlineTEnsor underlineDecomposition for binary and count tensors.
  arXiv  Detail & Related papers  (2024-01-15T14:27:03Z)
• Disentanglement via Latent Quantization [60.37109712033694]
  In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. We demonstrate the broad applicability of this approach by adding it to both basic data-re (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models.
  arXiv  Detail & Related papers  (2023-05-28T06:30:29Z)
• DIFFormer: Scalable (Graph) Transformers Induced by Energy Constrained Diffusion [66.21290235237808]
  We introduce an energy constrained diffusion model which encodes a batch of instances from a dataset into evolutionary states. We provide rigorous theory that implies closed-form optimal estimates for the pairwise diffusion strength among arbitrary instance pairs. Experiments highlight the wide applicability of our model as a general-purpose encoder backbone with superior performance in various tasks.
  arXiv  Detail & Related papers  (2023-01-23T15:18:54Z)
• Low-Rank Tensor Function Representation for Multi-Dimensional Data Recovery [52.21846313876592]
  Low-rank tensor function representation (LRTFR) can continuously represent data beyond meshgrid with infinite resolution. We develop two fundamental concepts for tensor functions, i.e., the tensor function rank and low-rank tensor function factorization. Our method substantiates the superiority and versatility of our method as compared with state-of-the-art methods.
  arXiv  Detail & Related papers  (2022-12-01T04:00:38Z)
• Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques [0.0]
  Natural convection in porous media is a highly nonlinear multiphysical problem relevant to many engineering applications. We present a non-intrusive reduced order model of natural convection in porous media employing deep convolutional autoencoders.
  arXiv  Detail & Related papers  (2021-07-23T20:58:15Z)
• Generative Model without Prior Distribution Matching [26.91643368299913]
  Variational Autoencoder (VAE) and its variations are classic generative models by learning a low-dimensional latent representation to satisfy some prior distribution. We propose to let the prior match the embedding distribution rather than imposing the latent variables to fit the prior.
  arXiv  Detail & Related papers  (2020-09-23T09:33:24Z)
• Learning Bijective Feature Maps for Linear ICA [73.85904548374575]
  We show that existing probabilistic deep generative models (DGMs) which are tailor-made for image data, underperform on non-linear ICA tasks. To address this, we propose a DGM which combines bijective feature maps with a linear ICA model to learn interpretable latent structures for high-dimensional data. We create models that converge quickly, are easy to train, and achieve better unsupervised latent factor discovery than flow-based models, linear ICA, and Variational Autoencoders on images.
  arXiv  Detail & Related papers  (2020-02-18T17:58:07Z)

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.