arXiv Machine Learning June 17, 2026 By Andrew Gracyk

Variational autoencoders with latent high-dimensional steady geometric flows for dynamics

Read the original on arXiv Machine Learning →

arXiv:2410. 10137v5 Announce Type: replace Abstract: We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds.

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Geometry-Preserving Encoder/Decoder in Latent Generative Models

arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.

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diffusion benchmarks

arXiv AI

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Geometry-aware Latent Autoregressive Generative Model for PDEs in Complex Domains

The paper introduces GeoLAMP, a Geometry-aware Latent Autoregressive generative Model designed to solve multiphysics partial differential equations in highly irregular, micro‑scale tortuous geometries. GeoLAMP employs a dual‑encoder graph architecture to capture both global topology and fine‑scale geometry, transforms real‑space fields into compact latent representations, and uses a causal self‑attention transformer with flow matching for stable, scalable block‑wise autoregressive prediction. The model is evaluated on three benchmark datasets—reactive flow, heat convection, and elasticity—showing consistently low errors across the entire rollout horizon.

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llms diffusion benchmarks

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arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.

By Ingvild Askim Adde, Mary M. Maleckar, Gabriel Balaban

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arXiv Machine Learning

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Disentangled Latent Dynamics Manifold Fusion for Solving Parameterized PDEs

arXiv:2603. 12676v3 Announce Type: replace Abstract: Generalizing neural surrogate models across different PDE parameters remains difficult because changes in PDE coefficients often make learning harder and optimization less stable.

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arXiv Machine Learning

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Geodesic Calculus on Implicitly Defined Latent Manifolds

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By Florine Hartwig, Josua Sassen, Juliane Braunsmann, Martin Rumpf, Benedikt Wirth

diffusion

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STREAM: Stochastic Riemannian Flow Matching with Anisotropic Decoder for Digital Histopathology Image Generation

arXiv:2606. 07036v1 Announce Type: cross Abstract: Synthetic histopathology image generation addresses critical challenges in computational pathology, including patient privacy and the growing need for large-scale training data for foundation models.

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