Source
Albergo, Boffi and Vanden-Eijnden (2023), LIT-645 — ARXIV-2303.08797. The framework paper introduces it: one learned velocity and score give a family of SDEs sharing the interpolant’s marginals, and its v1 abstract says the noise strength “can be tuned as model hyper-parameter after training”. Its evidence is a 2-D checkerboard and a 128-D Gaussian mixture.
Ma et al. (2024), LIT-447 — ARXIV-2401.08740. Shares three authors with the framework, takes its KL bound to derive a computable coefficient, and supplies the ImageNet measurement.
The claim is structural before it is empirical
In score-based diffusion the reverse-time SDE’s diffusion coefficient is taken from the forward SDE that generated the training distribution, and the literature presents this inheritance as intrinsic to the method.
It is not. The coefficient enters the integration of the reverse process and appears in neither the velocity field nor the score — the two things training estimates. So it is a knob on the sampler, not on the model, and it can be chosen after training with no retraining, by whatever criterion you like.
That is why this is Active on one group’s evidence: the load-bearing part
is an identity, not a sweep. The sweep confirms the identity buys something.
What it buys
Tuning it tightens control of the KL divergence between the model distribution and the target, and the empirical gain is a step in SiT’s transition from DiT — measured with the model frozen, at matched function evaluations.
The free-lunch framing is the useful one. Most practitioners with a trained diffusion model have an unexploited tuning dimension that costs sampling passes rather than training runs.
The precondition nobody states
The freedom is usable because training is in continuous time. Continuous time is the step in SiT’s transition whose direct gain is marginal, and this is what it is actually for: it decouples the sampling discretization from the training discretization, so the integration can be re-chosen after the fact. A discrete-time model has already committed.
That makes SOTA-266’s and this practice’s cases interlock — a marginal-looking choice earns its place by what it leaves open.
Against the record’s assumption about samplers
Every sampler practice the record holds treats sampling as downstream of training: SOTA-203 picks a higher-order ODE solver for the weights you have, SOTA-207 picks the deterministic sampler when the noise input has to mean something. Both are about choosing among samplers given a trained model. This says one parameter of the stochastic sampler was never determined by training at all, which is a different kind of freedom than choosing a solver.
Conditions
Measured on class-conditional ImageNet at 256×256 and 512×512, with FID as the only quality metric. The identity generalizes; the size of the gain is one dataset’s.
The coefficient may need regularizing near an endpoint for some interpolants — the linear and GVP interpolants carry a term that makes the SDE hard to integrate there — so “free to choose” is free within a range that the interpolant sets.
The criterion can be something other than sample quality. Flow-GRPO (LIT-779) sets the coefficient on a frozen flow-matching model to make its sampler a Gaussian policy that explores, and picks a = 0.7 by how fast an RL reward rises; too much noise drives images to zero reward. That uses the freedom this practice describes and measures nothing about what it buys in FID.
Requires a stochastic sampler. A deterministic ODE sampler has no diffusion coefficient to tune, so this and SOTA-207 apply in different cases rather than competing.
Known implementations
- SiT-XL, which reports its FID with the coefficient tuned.