Volterra Generative Models

• URL: http://arxiv.org/abs/2606.18071v1
• Date: Tue, 16 Jun 2026 15:40:09 GMT
• Title: Volterra Generative Models
• Abstract summary: We introduce Volterra generative models, a continuous-time score-based framework whose forward process injects path-dependent noise through fractional kernels.<n>We prove squared error bounds, derive an augmented linear-Gaussian forward process, and show that the learning can remain data-dimensional.<n>Experiments on MNIST and CIFAR-10 show that persistent fractional perturbations with small Markovian lifts can improve score-based generation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Score-based diffusion models typically use Brownian perturbations, which provide tractable reverse-time dynamics but impose memoryless noising. We introduce Volterra generative models, a continuous-time score-based framework whose forward process injects path-dependent noise through fractional kernels. To handle the non-Markovian and non-semimartingale dynamics, we construct finite-dimensional Markovian lifts using Gaussian quadrature in both regimes and a hybrid finite-difference exponential approximation in the smooth regime. We prove squared error bounds, derive an augmented linear-Gaussian forward process, and show that the learning can remain data-dimensional by considering residual states and analytic auxiliary Gaussian scores. We also identify covariance and reverse-time degeneracies caused by shared Brownian factors and signed smooth-regime weights. The degeneracy motivates stabilized conditioning and, for stiff larger lifts, a Gaussian-bridge reconstruction sampler. Experiments on MNIST and CIFAR-10 show that persistent fractional perturbations with small Markovian lifts can improve score-based generation on MNIST and provide a promising extension to natural images, while the bridge sampler provides a stability mechanism for larger lifts.

Related papers

• More Experts, Worse Dynamics: Inverse Scaling and Spectral Bias in Mixture-of-Experts State-Space Models [0.0]
  We study a next-step prediction task on sequences composed of three regimes.<n>Operator-level mixture models consistently fail to outperform a single-expert baseline.
  arXiv  Detail & Related papers  (2026-08-22T08:22:32Z)
• Generator-Guided Inverse Sampling for Lévy-Driven Generative Models [7.926964418680483]
  We study inverse sampling for Lévy-driven generative models from the perspective of Markov generators.<n>We develop a structured reverse sampler that decomposes the dynamics into diffusion, small jump, and large jump components.
  arXiv  Detail & Related papers  (2026-08-11T02:25:28Z)
• Inspectable Neural Markov Models for Non-Stationary Time Series [0.0]
  We propose a hybrid approach that parameterizes the manifold of Markov chains through a neural network.<n>We show that conditioning on realized volatility produces a more internally consistent Markovian structure than return-based states.
  arXiv  Detail & Related papers  (2026-05-29T07:29:35Z)
• Next-Acceleration-Scale Prediction for Autoregressive MRI Reconstruction [52.32112533846212]
  MRI reconstruction is an inherently ill-posed inverse problem, since incomplete measurements admit many plausible solutions.<n>We address this limitation by moving reconstruction to discrete multi-scale latent space and posing it as autoregressive next-acceleration-scale prediction.<n>We show that our approach delivers improved reconstruction performance across diverse sampling patterns under extreme undersampling.
  arXiv  Detail & Related papers  (2026-05-19T04:40:50Z)
• Hypergraph Generation via Structured Stochastic Diffusion [8.501793261157966]
  HEDGE is a generative model defined directly on relaxed incidence matrices.<n> conditional means, scores, and reverse-drift targets are available in closed form.<n>We show improved hypergraph generation quality relative to strong baselines.
  arXiv  Detail & Related papers  (2026-05-06T15:19:20Z)
• Generative Path-Law Jump-Diffusion: Sequential MMD-Gradient Flows and Generalisation Bounds in Marcus-Signature RKHS [0.0]
  This paper introduces a novel generative framework for synthesising cdlg trajectories that are sequentially consistent with time-evolving path-law proxies.<n>We develop the textitAnticipatory Neural Jump-Diffusion (ANJD) flow, a generative mechanism that effectively inverts the time-extended Marcus-sense signature.
  arXiv  Detail & Related papers  (2026-04-06T13:23:59Z)
• KoopGen: Koopman Generator Networks for Representing and Predicting Dynamical Systems with Continuous Spectra [65.11254608352982]
  We introduce a generator-based neural Koopman framework that models dynamics through a structured, state-dependent representation of Koopman generators.<n>By exploiting the intrinsic Cartesian decomposition into skew-adjoint and self-adjoint components, KoopGen separates conservative transport from irreversible dissipation.
  arXiv  Detail & Related papers  (2026-02-15T06:32:23Z)
• Generative Model Inversion Through the Lens of the Manifold Hypothesis [98.37040155914595]
  Model inversion attacks (MIAs) aim to reconstruct class-representative samples from trained models.<n>Recent generative MIAs utilize generative adversarial networks to learn image priors that guide the inversion process.
  arXiv  Detail & Related papers  (2025-09-24T14:39:25Z)
• Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling [0.0]
  We present a data-driven framework for estimating the response of higher-order moments of nonlinear systems to small external perturbations.<n>We combine GFDT with score-based generative modeling to estimate the system's score function directly from data.<n>Our method is validated on several models relevant to climate dynamics.
  arXiv  Detail & Related papers  (2025-04-17T20:54:33Z)
• One-for-More: Continual Diffusion Model for Anomaly Detection [63.50488826645681]
  Anomaly detection methods utilize diffusion models to generate or reconstruct normal samples when given arbitrary anomaly images.<n>Our study found that the diffusion model suffers from severe faithfulness hallucination'' and catastrophic forgetting''<n>We propose a continual diffusion model that uses gradient projection to achieve stable continual learning.
  arXiv  Detail & Related papers  (2025-02-27T07:47:27Z)
• Generative Fractional Diffusion Models [53.36835573822926]
  We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Our evaluations on real image datasets demonstrate that GFDM achieves greater pixel-wise diversity and enhanced image quality, as indicated by a lower FID.
  arXiv  Detail & Related papers  (2023-10-26T17:53:24Z)
• Haar Wavelet based Block Autoregressive Flows for Trajectories [129.37479472754083]
  Prediction of trajectories such as that of pedestrians is crucial to the performance of autonomous agents. We introduce a novel Haar wavelet based block autoregressive model leveraging split couplings. We illustrate the advantages of our approach for generating diverse and accurate trajectories on two real-world datasets.
  arXiv  Detail & Related papers  (2020-09-21T13:57:10Z)

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.