The paper investigates how generative models for implied volatility surfaces must respect static no‑arbitrage constraints. By mapping latent codes to surfaces, it defines a scalar margin for each code and identifies the admissible latent set where this margin is nonnegative. The authors prove that admissible codes remain admissible under small perturbations, characterize the boundary via a zero‑margin condition, and derive a level‑set equation guiding dynamics toward this boundary. The framework applies broadly to models such as variational autoencoders and GANs, and numerical experiments confirm known boundaries in analytic examples and demonstrate how the boundary can correct violating latent codes.
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.
arXiv:2501. 09876v3 Announce Type: replace-cross Abstract: Generative modeling aims to generate new data samples that resemble a given dataset.
arXiv:2112.09646v2 Announce Type: replace Abstract: The generation of discontinuous distributions is a difficult task for most known frameworks such as generative autoencoders and generative adversar...
arXiv:2606. 08953v1 Announce Type: new Abstract: Modern generative models often define an entire probability path from a simple prior to the data law, rather than only an endpoint map.
arXiv:2608.29335v1 Announce Type: new Abstract: Latent generative models typically follow a two-stage pipeline, training a variational autoencoder for reconstruction and then a generative model on th...
arXiv:2607. 23182v1 Announce Type: cross Abstract: We prove the identifiability of deep generative models (DGMs) with piecewise-affine (PWA) decoders and Gaussian mixture model (GMM) priors, in a purely unsupervised setting.
arXiv:2510. 09468v3 Announce Type: replace Abstract: Latent manifolds of autoencoders provide low-dimensional representations of data, which can be studied from a geometric perspective.
arXiv:2609.31570v1 Announce Type: new Abstract: Deep learning has substantially accelerated the calibration of complex stochastic-volatility models, but neural point calibration alone does not captur...
arXiv:2408. 15344v2 Announce Type: replace Abstract: Many scientific and engineering problems involve observing a common phenomenon through multiple heterogeneous sensors or measurement modalities.
The paper introduces a new method for perturbing data distributions in a way that respects equality constraints, allowing generative models to better handle constrained data. By adjusting the distribution while preserving the manifold geometry, the approach ensures support matches the ambient space dimension. Experiments with diffusion models and normalizing flows demonstrate improved data recovery and stable sampling across several tasks.
arXiv:2508. 09156v3 Announce Type: replace-cross Abstract: We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems.
arXiv:2605. 12764v3 Announce Type: replace-cross Abstract: This paper introduces a physics-informed generative framework that resolves the fundamental conflict between the statistical flexibility of deep learning and the rigorous theoretical constraints of fixed-income modeling.