Both at Once: A Reference-Process Framework for Simulation-Free, Finite-Time Diffusion

Generative diffusion models usually force a trade: simulation-free training or finite-time sampling, rarely both. A paper posted to arXiv on August 4, 2026 argues that trade is an artifact of reference-process design — not a law of diffusion.

Kentaro Kaba, Masayuki Ohzeki, and Yuki Sughiyama propose a framework that prescribes tractable time-dependent conditional distributions, then constructs a reference diffusion process whose marginals match them. The result, they report, delivers simulation-free training and finite-time generation simultaneously.

Why the reference process matters

Diffusion performance depends on how the reference process connects empirical data to the prior. Conventional choices optimize one axis at the expense of the other.

The authors' key move: design the reference so marginals are known and tractable at each time step, then derive training objectives from that structure.

Score matching as reversal, not axiom

A central theoretical claim: score matching is not fundamental to diffusion training. It emerges naturally when reversing the prescribed reference process.

That reframes a pillar of modern generative modeling as a consequence of process design rather than a starting assumption.

Connection to flow matching

The paper further shows conditional flow matching arises as the small-noise limit of the proposed framework — linking diffusion and flow-matching literature through a shared reference-process lens.

What is verified today

This is an arXiv preprint (2608.03117v1). The authors present a unified design framework and theoretical connections; empirical benchmarks on large-scale image or video generation are not the focus of the abstract.

Peer review and independent replication will determine whether the finite-time + simulation-free combination holds at production scale.

Why it matters for practitioners

If the framework generalizes, teams training diffusion models could:

• Avoid expensive simulation loops during training
• Sample in finite steps without the quality penalties often associated with shortened schedules
• Transfer insights between diffusion and flow-matching pipelines via shared reference-process tooling

Open questions

• How does the method compare to established samplers on standard image benchmarks?
• Does the tractable-marginal construction extend cleanly to text, video, or multimodal latents?
• Which reference processes remain practical when data dimensionality grows?

The paper is available on arXiv with PDF and TeX source.

### Sources

• arXiv — Simulation-free and finite-time diffusion model (2608.03117v1) (August 4, 2026)
• arXiv DOI — 10.48550/arXiv.2608.03117 (August 2026)