Song and colleagues: consistency models support one-step and few-step generation

What changed

A boundary-constrainedtrajectory-endpoint map supports one/fewstep generation, teacher distillation anddirect-data training interface; originalfiniteexperiments andlaterCTargumentlimits separated.

Scientific scope

A boundary-constrainedtrajectory-endpoint map supports one/fewstep generation, teacher distillation anddirect-data training interface; originalfiniteexperiments andlaterCTargumentlimits separated. The target is arXiv 2303.01469v2. Consistency distillation and direct training have different assumptions and costs. The endpoint is smoothed and approximate; the theoretical bounds require the paper’s regularity, boundary and discretization conditions and do not guarantee successful optimization. A later Song–Dhariwal point-mass counterexample exposes a problem in the unequal-teacher moving-average justification for original direct training. Its corrected justification and improved benchmark scores are credited separately. Editing examples may use many steps. WRS has not replayed the image benchmarks or certified every theorem.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

• Yang Song · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• Prafulla Dhariwal · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• Mark Chen · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.
• Ilya Sutskever · SCIENCE: Original source-listed scientific author of this scoped work; byline does not determine effort fractions.

• Song, Dhariwal, Chen and Sutskever, Consistency Models; exactar Xiv 2303.01469 v 2
• Original Consistencymodels officialar Xiv completebyline/versiondates
• Song and Dhariwal, Improved Techniques for Training Consistency Models; selectedrelatedcorrection only

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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