Symmetry-Preserving Diffusion Models via Target Symmetrization

• URL: http://arxiv.org/abs/2502.09890v1
• Date: Fri, 14 Feb 2025 03:26:57 GMT
• Title: Symmetry-Preserving Diffusion Models via Target Symmetrization
• Authors: Vinh Tong, Yun Ye, Trung-Dung Hoang, Anji Liu, Guy Van den Broeck, Mathias Niepert,
• Abstract summary: We propose a novel approach that enforces equivariance through a symmetrized loss function.<n>Our method uses Monte Carlo sampling to estimate the average, incurring minimal computational overhead.<n> Experiments show improved sample quality compared to existing methods.
• Score: 43.83899968118655
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Diffusion models are powerful tools for capturing complex distributions, but modeling data with inherent symmetries, such as molecular structures, remains challenging. Equivariant denoisers are commonly used to address this, but they introduce architectural complexity and optimization challenges, including noisy gradients and convergence issues. We propose a novel approach that enforces equivariance through a symmetrized loss function, which applies a time-dependent weighted averaging operation over group actions to the model's prediction target. This ensures equivariance without explicit architectural constraints and reduces gradient variance, leading to more stable and efficient optimization. Our method uses Monte Carlo sampling to estimate the average, incurring minimal computational overhead. We provide theoretical guarantees of equivariance for the minimizer of our loss function and demonstrate its effectiveness on synthetic datasets and the molecular conformation generation task using the GEOM-QM9 dataset. Experiments show improved sample quality compared to existing methods, highlighting the potential of our approach to enhance the scalability and practicality of equivariant diffusion models in generative tasks.

Related papers

• Zero-Variance Gradients for Variational Autoencoders [32.818968022327866]
  Training deep generative models like Variational Autoencoders (VAEs) is often hindered by the need to backpropagate gradients through sampling of their latent variables.<n>In this paper, we propose a new perspective that sidesteps this problem, which we call Silent Gradients.<n>Instead of improving estimators, we leverage specific decoder architectures analytically to compute the expected ELBO, yielding a gradient with zero variance.
  arXiv  Detail & Related papers  (2025-08-05T15:54:21Z)
• Learning (Approximately) Equivariant Networks via Constrained Optimization [25.51476313302483]
  Equivariant neural networks are designed to respect symmetries through their architecture.<n>Real-world data often departs from perfect symmetry because of noise, structural variation, measurement bias, or other symmetry-breaking effects.<n>We introduce Adaptive Constrained Equivariance (ACE), a constrained optimization approach that starts with a flexible, non-equivariant model.
  arXiv  Detail & Related papers  (2025-05-19T18:08:09Z)
• Energy-Based Coarse-Graining in Molecular Dynamics: A Flow-Based Framework Without Data [0.0]
  We introduce a data-free generative framework for coarse-graining that directly targets the all-atom Boltzmann distribution.<n>A potentially learnable, bijective map from the full latent space to the all-atom configuration space enables automatic and accurate reconstruction of molecular structures.
  arXiv  Detail & Related papers  (2025-04-29T17:05:27Z)
• Preconditioned Inexact Stochastic ADMM for Deep Model [35.37705488695026]
  This paper develops an algorithm, PISA, which enables scalable parallel computing and supports various second-moment schemes. Grounded in rigorous theoretical guarantees, the algorithm converges under the sole assumption of Lipschitz of the gradient. Comprehensive experimental evaluations for or fine-tuning diverse FMs, including vision models, large language models, reinforcement learning models, generative adversarial networks, and recurrent neural networks, demonstrate its superior numerical performance compared to various state-of-the-art Directions.
  arXiv  Detail & Related papers  (2025-02-15T12:28:51Z)
• Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations [1.371691382573869]
  We develop and enhance score-based diffusion models in field reconstruction tasks. We introduce a condition encoding approach to construct a tractable mapping mapping between observed and unobserved regions. We demonstrate the ability of the model to capture possible reconstructions and improve the accuracy of fused results.
  arXiv  Detail & Related papers  (2024-08-30T19:46:23Z)
• Improving Equivariant Model Training via Constraint Relaxation [31.507956579770088]
  We propose a novel framework for improving the optimization of such models by relaxing the hard equivariance constraint during training.<n>We provide experimental results on different state-of-the-art network architectures, demonstrating how this training framework can result in equivariant models with improved generalization performance.
  arXiv  Detail & Related papers  (2024-08-23T17:35:08Z)
• Uniform Transformation: Refining Latent Representation in Variational Autoencoders [7.4316292428754105]
  We introduce a novel adaptable three-stage Uniform Transformation (UT) module to address irregular latent distributions. By reconfiguring irregular distributions into a uniform distribution in the latent space, our approach significantly enhances the disentanglement and interpretability of latent representations. Empirical evaluations demonstrated the efficacy of our proposed UT module in improving disentanglement metrics across benchmark datasets.
  arXiv  Detail & Related papers  (2024-07-02T21:46:23Z)
• On the Trajectory Regularity of ODE-based Diffusion Sampling [79.17334230868693]
  Diffusion-based generative models use differential equations to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models.
  arXiv  Detail & Related papers  (2024-05-18T15:59:41Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  We present a unifying perspective on recent results on ridge regression.<n>We use the basic tools of random matrix theory and free probability, aimed at readers with backgrounds in physics and deep learning.<n>Our results extend and provide a unifying perspective on earlier models of scaling laws.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference [47.460898983429374]
  We introduce an ensemble Kalman filter (EnKF) into the non-mean-field (NMF) variational inference framework to approximate the posterior distribution of the latent states. This novel marriage between EnKF and GPSSM not only eliminates the need for extensive parameterization in learning variational distributions, but also enables an interpretable, closed-form approximation of the evidence lower bound (ELBO) We demonstrate that the resulting EnKF-aided online algorithm embodies a principled objective function by ensuring data-fitting accuracy while incorporating model regularizations to mitigate overfitting.
  arXiv  Detail & Related papers  (2023-12-10T15:22:30Z)
• Multi-Response Heteroscedastic Gaussian Process Models and Their Inference [1.52292571922932]
  We propose a novel framework for the modeling of heteroscedastic covariance functions. We employ variational inference to approximate the posterior and facilitate posterior predictive modeling. We show that our proposed framework offers a robust and versatile tool for a wide array of applications.
  arXiv  Detail & Related papers  (2023-08-29T15:06:47Z)
• Efficient Training of Energy-Based Models Using Jarzynski Equality [13.636994997309307]
  Energy-based models (EBMs) are generative models inspired by statistical physics. The computation of its gradient with respect to the model parameters requires sampling the model distribution. Here we show how results for nonequilibrium thermodynamics based on Jarzynski equality can be used to perform this computation efficiently.
  arXiv  Detail & Related papers  (2023-05-30T21:07:52Z)
• Reflected Diffusion Models [93.26107023470979]
  We present Reflected Diffusion Models, which reverse a reflected differential equation evolving on the support of the data. Our approach learns the score function through a generalized score matching loss and extends key components of standard diffusion models.
  arXiv  Detail & Related papers  (2023-04-10T17:54:38Z)
• ClusterQ: Semantic Feature Distribution Alignment for Data-Free Quantization [111.12063632743013]
  We propose a new and effective data-free quantization method termed ClusterQ. To obtain high inter-class separability of semantic features, we cluster and align the feature distribution statistics. We also incorporate the intra-class variance to solve class-wise mode collapse.
  arXiv  Detail & Related papers  (2022-04-30T06:58:56Z)
• Equivariant vector field network for many-body system modeling [65.22203086172019]
  Equivariant Vector Field Network (EVFN) is built on a novel equivariant basis and the associated scalarization and vectorization layers. We evaluate our method on predicting trajectories of simulated Newton mechanics systems with both full and partially observed data.
  arXiv  Detail & Related papers  (2021-10-26T14:26:25Z)
• A data-driven peridynamic continuum model for upscaling molecular dynamics [3.1196544696082613]
  We propose a learning framework to extract, from molecular dynamics data, an optimal Linear Peridynamic Solid model. We provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training.
  arXiv  Detail & Related papers  (2021-08-04T07:07:47Z)
• EBM-Fold: Fully-Differentiable Protein Folding Powered by Energy-based Models [53.17320541056843]
  We propose a fully-differentiable approach for protein structure optimization, guided by a data-driven generative network. Our EBM-Fold approach can efficiently produce high-quality decoys, compared against traditional Rosetta-based structure optimization routines.
  arXiv  Detail & Related papers  (2021-05-11T03:40:29Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)
• Learning Invariances in Neural Networks [51.20867785006147]
  We show how to parameterize a distribution over augmentations and optimize the training loss simultaneously with respect to the network parameters and augmentation parameters. We can recover the correct set and extent of invariances on image classification, regression, segmentation, and molecular property prediction from a large space of augmentations.
  arXiv  Detail & Related papers  (2020-10-22T17:18:48Z)
• Neural Control Variates [71.42768823631918]
  We show that a set of neural networks can face the challenge of finding a good approximation of the integrand. We derive a theoretically optimal, variance-minimizing loss function, and propose an alternative, composite loss for stable online training in practice. Specifically, we show that the learned light-field approximation is of sufficient quality for high-order bounces, allowing us to omit the error correction and thereby dramatically reduce the noise at the cost of negligible visible bias.
  arXiv  Detail & Related papers  (2020-06-02T11:17:55Z)

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.