arXiv:2606.18071v1 Announce Type: cross 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
The paper addresses fundamental limitations in current diffusion models, indicating an ongoing push for more sophisticated and robust AI generative processes.
This development could lead to more powerful and versatile generative AI, impacting various applications from synthetic data creation to complex system simulation.
The introduction of Volterra generative models moves beyond memoryless noising, offering a new framework for continuous-time score-based generative AI with path-dependent noise.
- · AI research institutions
- · Generative AI developers
- · Industries relying on synthetic data
- · Developers stuck with older diffusion model paradigms
Improved generative model accuracy and capability for complex data distributions.
Accelerated development of AI applications requiring high fidelity and nuanced generative abilities.
New frontiers in AI-driven design, simulation, and scientific discovery due to enhanced modeling power.
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Read at arXiv cs.AI