The paper introduces a method for creating generative diffusion surrogates that use an analytically derived variance schedule based on the time derivative of known variance from macroscopic theory or empirical scaling. By enforcing this variance path, the model can capture non‑Gaussian structure in transport systems without requiring intermediate‑time physical data. The approach is validated on ballistic‑to‑diffusive transport in turbulent plasmas, accurately reproducing test‑particle distributions, laboratory‑measured variance, and simulated kurtosis evolution.
arXiv:2601. 13602v3 Announce Type: replace-cross Abstract: This paper introduces an analytical approach to quantifying and optimizing the distributional discrepancy in generative diffusion models.
arXiv:2609.38438v1 Announce Type: cross Abstract: Machine learning surrogate models offer a promising path toward accelerating plasma turbulence simulations. We present PreVAE-Turb, a surrogate model...
arXiv:2608. 02575v1 Announce Type: new Abstract: Diffusion models rely on stochastic inputs, yet on finite-precision hardware, the "randomness" they consume is realized as deterministic numerical orbits generated by pseudorandom rules.
arXiv:2605. 05540v2 Announce Type: replace Abstract: Fast surrogate modeling for high-dimensional physical dynamics requires more than low short-term error: useful models must roll out efficiently while preserving the statistical structure of long trajectories.
The book "The Principles of Diffusion Models" outlines the foundational concepts behind diffusion models, tracing their evolution from a forward process that corrupts data into noise to a reverse process that reconstructs data. It presents three complementary perspectives—variational, score-based, and flow-based—each describing how a time-dependent velocity field transports a simple prior to the data distribution. The text also covers practical guidance for controllable generation, efficient solvers, and diffusion-inspired flow-map models, providing a mathematically grounded framework for readers with basic deep‑learning knowledge.
arXiv:2512.20003v2 Announce Type: replace Abstract: Sampling from unnormalized probability densities is a pervasive challenge across the computational and physical sciences. Diffusion models provide...
arXiv:2608. 02799v1 Announce Type: cross Abstract: Score-based diffusion models are typically formulated using continuous-time stochastic differential equations and measure-theoretic stochastic calculus.
arXiv:2608. 15144v1 Announce Type: cross Abstract: Posterior sampling with a pretrained diffusion prior is governed by a conditional score whose intermediate likelihood component is generally intractable.
arXiv:2602. 17706v2 Announce Type: replace Abstract: Diffusion models learn data distributions indirectly through denoising, making the difficulty of generative modeling closely tied to the dependency structure of data.
arXiv:2601. 21026v2 Announce Type: replace-cross Abstract: Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics.
arXiv:2607. 03517v1 Announce Type: new Abstract: Brownian Bridge Diffusion Models (BBDM) offer an appealing framework for image restoration and inverse problems by constructing a stochastic bridge from the clean signal directly to the degraded observation, rather than to pure noise.
arXiv:2607. 00196v1 Announce Type: new Abstract: Many scientific systems exhibit uncertainty from stochastic forcing, unresolved degrees of freedom, or imperfect observations, making reliable surrogate forecasting fundamentally distributional rather than pointwise.