Frans, Hafner, Levine and Abbeel, UC Berkeley (2024), ICLR 2025 — ARXIV-2410.12557. Read at v3 (23 Jun 2025), main text and Appendices A–B; v1 is 16 Oct 2024.
Key takeaways
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One network, one run, a step-size input (§3, Eqs. 3–5, Alg. 1). The model s(x_t, t, d) predicts the normalized jump to x_{t+d}. At d = 0 it is trained on the ordinary flow-matching target x₁ − x₀. For d > 0 the target for a step of 2d is the mean of two consecutive d-steps taken by the model itself, under stop-gradient and with EMA weights (§3.1). With M = 128 there are eight step sizes, 1/128 to 1. A quarter of each batch carries self-consistency targets. Counting a backward pass as two forwards, the cost is about 16% over plain flow matching (§3.1, footnote 2).
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The argument for it is that flow matching cannot take big steps even at its optimum (§2, Fig. 2). The learned velocity at t = 0 points at the dataset mean, so a one-step Euler jump collapses a multimodal target. Plain flow matching scores 280.5 and 324.8 FID at one step (Table 1).
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The matched comparison (Table 1, DiT-B, one codebase, “equal or greater” compute, App. B.2). FID-50k at 128 / 4 / 1 steps:
Method CelebA-HQ-256 ImageNet-256 Flow matching 7.3 / (63.3) / (280.5) 17.3 / (108.2) / (324.8) Reflow 16.1 / 18.4 / 23.2 16.9 / 32.8 / 44.8 Progressive distillation (302.9) / (251.3) / 14.8 (201.9) / (142.5) / 35.6 Consistency distillation 59.5 / 39.6 / 38.2 132.8 / 98.01 / 136.5 Consistency training 53.7 / 19.0 / 33.2 42.8 / 43.0 / 69.7 Shortcut 6.9 / 13.8 / 20.5 15.5 / 28.3 / 40.3 Parentheses mark step counts the method is not meant for.
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Stability comes from weight decay and EMA targets, not a schedule (§3.1, §6). Weight decay 0.1 is called “crucial”, because early self-generated targets are noise the model can latch onto. EMA weights for the targets damp oscillation at d = 1. Guidance (CFG 1.5 on ImageNet) is used only at d = 0 and fixed before training (§3.1, Fig. 9).
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At DiT-XL size, 3.8 / 7.8 / 10.6 FID at 128 / 4 / 1 steps on ImageNet-256 (Table 2). One-step FID falls with model size (Fig. 5, curve only).
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Robot control in one call (§5.5, Fig. 7). Swapping the diffusion policy for a shortcut policy, with weight decay raised to 0.1, scores 0.87 on Push-T and 0.80 on Transport at one step. The 100-step diffusion policy scores 0.95 and 1.00, and the same policy run at one step 0.12 and 0.00.
Where the hedges are
Per DP-010:
- “Shortcut models consistently produce higher quality samples than previous approaches, such as consistency models and reflow” (abstract). True of every row in Table 1 except progressive distillation, which wins at one step on both datasets (14.8 against 20.5, 35.6 against 40.3). §5.1 says so; the abstract does not.
- The consistency baselines are not the published methods at their published strength. Both are re-run in velocity space with an L2 loss (App. B.2). Consistency training uses a binary-time schedule, not the original’s, and not the improved recipe of LIT-786. Consistency distillation scores 132.8 at 128 steps on ImageNet, worse than the undistilled diffusion row. The table measures these methods as implemented here.
- “Equal or greater” compute is asserted, not tabled (App. B.2). The two-stage methods distil a 400K-iteration flow-matching checkpoint for another 400K iterations. Live reflow is said to take over four times the compute. No run’s FLOPs or wall-clock are reported.
- Table 2 says 250 epochs for the XL model. Appendix B gives 800K iterations at batch 256, about 160 passes over ImageNet’s 1.28M images. The gap is not explained.
- “A slightly better FID than a comparable flow-matching model” (§5.1): 6.9 against 7.3 and 15.5 against 17.3, one run each. The authors offer implicit regularization as a “blind hypothesis”.
- One FID per cell, no seeds, no precision or recall. The scaling result is a figure without values.
Which comparisons are like for like
- Table 1 is the paper’s controlled comparison: same DiT-B, same VAE latents, same optimizer and constant learning rate, all methods trained from scratch or from the same flow-matching teacher. Its weak point is the consistency rows, as above.
- Table 2 sets the XL shortcut model against DiT-XL, ADM, LDM and GANs at their own budgets. The caption says the budgets differ.
Standing in the anthology
It takes its self-consistency targets from EMA weights, the opposite choice to SOTA-446, and does not ablate it.
It extends Rectified Flow (LIT-636). The d = 0 term is that paper’s straight-path velocity regression, which the authors adopt “for simplicity” (§2). The step-size input and self-consistency targets are added on top, so that one network learns both the flow and jumps along it. Reflow, Rectified Flow’s own straightening procedure, is one of the Table 1 baselines, trained on 50K and 1M teacher-generated pairs (App. B.2).
The other baselines are re-implementations under Table 1’s matched setup: progressive distillation (LIT-067), halving the step count in eight 50K phases; consistency distillation and consistency training after Consistency Models (LIT-093); and a DiT-B diffusion model following DiT (LIT-448), 39.7 FID at 128 steps.
On SOTA-206 it is direct support. One set of weights serves 1, 4 and 128 steps, and many-step quality is not lost (6.9 against flow matching’s 7.3). §5.2 recommends the dial as a workflow: regenerate a one-step image from the same noise with more steps to refine it. Progressive distillation is the counter-case in the same table. It is the better one-step model and has no many-step mode. Keeping the dial cost 5.7 FID on CelebA-HQ and 4.7 on ImageNet at one step here.
On SOTA-392 it is adjacent evidence, not the test that practice asks for. The teacher is a flow-matching model, a 1-rectified flow. Distilling it progressively, with no reflow, beats one reflow at one step on both datasets (14.8 against 23.2, 35.6 against 44.8), at roughly matched compute and at 256 px. Reflow’s many-step cost shows on CelebA-HQ (7.3 to 16.1) but not on ImageNet (17.3 to 16.9). Reflow followed by distillation, the arm SOTA-392 needs, is not run.
MeanFlow (LIT-784) and Inductive Moment Matching (LIT-775) both compare against this paper’s DiT-XL row, 10.60 at one step, and both condition on two times as it does.
Filed without a NOTE: the takeaways come from one full reading done for this filing, of v3’s main text and appendices. Fig. 4 and Fig. 5 are read only where the text gives numbers.