Topics — The twenty-eight kinds of claim this anthology files against — the primary axis of both the practice registry and the reading list, and the same twenty-eight for each (ADR-026). The filing rule is the point: take a domain topic when the claim is ABOUT the domain; a claim merely discovered in one still takes its kind. The axis organizes the record, it does not bound it: content the list cannot place is evidence the list is short (ADR-059).
Few-step generation — getting a sample in one or a few network evaluations — progressive, distribution-matching and adversarial distillation, consistency, flow-map, shortcut and mean-flow models, and fast ODE solvers. A subtopic, worn beside generative-modeling or inference-optimization.
5 of 129 THEORY documents. Back to the full index.
| # | Title | Summary | Status |
|---|---|---|---|
| THEORY-118 | Continuous-time consistency training is unstable through the time derivative in its tangent, and tangent normalization, which MeanFlow’s adaptive loss weight already is, controls it | Lu and Song (2024), LIT-790, §4.1–4.2. The continuous-time consistency gradient follows the tangent df/dt along the ODE. Of its parts, the authors find the time derivative of the network unstable, and derive why: EDM’s time transform contributes a factor 1/cos(t) that blows up at the noise end, and a large Fourier embedding scale oscillates. Normalizing the tangent caps the rest. Zheng et al. (LIT-783) find the same term fragile at 14B and in BF16, and state that MeanFlow’s adaptive weight with p = 1 is tangent normalization, which is checkable algebra. The localization is measured on CIFAR-10 gradient norms, and the fixes on one ImageNet-512 setting. | Proposed |
| THEORY-119 | Consistency, shortcut, MeanFlow and progressive-distillation models all estimate the two-time flow map of the probability-flow ODE, and differ in which identity of that map they train on | Boffi, Albergo and Vanden-Eijnden (2024), LIT-793. The object a few-step model learns is X_{s,t}, which carries any point of the ODE from time s to time t. It satisfies three identities: a Lagrangian equation in the end time, an Eulerian equation in the start time, and composition. Progressive distillation and shortcut models train on composition, consistency models and MeanFlow on the Eulerian equation, and flow map matching’s Lagrangian loss on the first. Consistency models are the one-time case. Inductive Moment Matching is the exception: it matches marginals, and its minimizer need not be the ODE’s map. Which identity trains best is measured once, on CIFAR-10, where the Lagrangian form won by a wide margin. | Active |
| THEORY-121 | Distribution-matching distillation loses coverage because it descends a reverse divergence on the student’s own samples, and a consistency term on teacher trajectories restores it | Lu and Song (2024), LIT-790, Fig. 7, and Zheng et al. (2025), LIT-783. DMD (LIT-643) descends KL(p_student ‖ p_teacher), evaluated on the student’s own samples. That direction penalizes mass where the teacher has none and is indifferent to a mode the student no longer produces. A consistency loss supervises points along the teacher’s trajectories that the student did not choose. On one backbone, sCM found distribution matching raising precision and losing recall as guidance rises, while consistency stayed near the teacher; read from the curves, the recall gap is already there at guidance 1. The account is rCM’s framing. That figure is its only measurement, from one group and one backbone, and DMD’s own authors give a different mechanism. | Proposed |
| THEORY-123 | A flow’s sampling ODE curves because the noise-data pairs it was trained on cross and the learned velocity averages them, so a coupling whose straight paths do not cross gives a straight flow | Pooladian et al. (2023), LIT-789, and Tong et al. (2023), LIT-798, with Rectified Flow, LIT-636. Flow matching regresses onto the velocity of a straight line between a paired noise and data point, so the learned field at (x, t) is the average of the velocities of every pair whose line passes through x at t. Under independent pairing many lines cross there, and the average turns. A coupling with no crossings, the OT plan in the limit or the flow’s own map after reflow, leaves one line through each point and a straight flow. The mechanism is proved. That this is what limits few-step image quality is measured only at 64 px and below, and Lee et al. (LIT-791) argue, without proof, that one reflow is enough. | Active |
| THEORY-124 | Consistency training is a bootstrapped fixed-point iteration, not descent on a loss, so a target that lags the student swamps a data signal that enters only at the order of the step | Song and Dhariwal (2023), LIT-786, Prop. 1, and Boffi, Albergo and Vanden-Eijnden (2024), LIT-793, Prop. 3.12. Consistency training compares the model at one noise level with a target at the next, and the data enter only through that small step. With the target’s weights equal to the student’s under stop-gradient, the scaled update converges to a regression onto the data. With any other target, such as an EMA, the limiting objective does not depend on the data at all. Proved on a one-point distribution, where it refutes the argument that justified EMA targets. That it is why EMA targets hurt on real data rests on one CIFAR-10 curve. | Proposed |