Source
Liu, Gong and Liu (2022), LIT-636, and Lipman et al. (2022), LIT-630, introduced the straight path concurrently. Albergo and Vanden-Eijnden’s stochastic interpolants (LIT-644) are a concurrent origin of the simulation-free objective but not of the straight path: they use a trigonometric interpolant and credit the linear one to Liu et al. Flow Matching contributes the first controlled comparison: the same U-Net, hyperparameters and epochs give CIFAR-10 FID 6.35 on the straight path against 8.06 on the diffusion path (its Table 1). The same comparison holds at ImageNet-32 and ImageNet-64 in the same table. It trained with uniform timesteps.
Ma et al. (2024), LIT-447 — ARXIV-2401.08740.
Esser et al. (2024), LIT-449 — ARXIV-2403.03206.
Both are load-bearing and they do different jobs. SiT is the controlled attribution: DiT’s architecture, parameter count and GFLOPs held exactly fixed while the interpolant is changed and nothing else. SD3 is the scale and the breadth: 61 formulations ranked, then the winner taken to 8B text-to-image with weights released. A practice on either alone would be weaker — one would be a small-scale ablation, the other a leaderboard entry.
In SiT (LIT-447) the walk from DiT changes one thing at a time on DiT’s backbone, and replacing the variance-preserving interpolant with a linear or GVP one is a significant FID gain on its own, alongside velocity prediction. SiT-XL ends at FID-50K 2.06 on class-conditional ImageNet 256×256. In SD3 (LIT-449) the 61 formulations are ranked on validation loss at matched settings: rectified flow with logit-normal timesteps comes first, and the uniform-timestep variant does not beat tuned ε-prediction. That ranking is the source of the title’s second half.
The Movie Gen team (2024), LIT-626, is the video evidence. At 5B, on video at 352×192, it compares flow matching against v-prediction diffusion with zero terminal SNR, with everything else held constant. Flow matching wins by a net +16.5 on human-rated quality and +7.1 on text alignment (its Table 8a). That is the only controlled comparison of the objective in the video line. Every other video report adopts it.
The diffusion arm Movie Gen beat is SOTA-422’s recipe: v-prediction on a schedule rescaled to zero terminal SNR, the repair for signal leaked at the last timestep. For a VP model the choice is between that repair and the straight path, which has zero terminal SNR by construction. In this one 5B video comparison the straight path won.
Both halves of the title are the practice
The straight line. Rectified flow connects data and noise along a straight path rather than the curved one a variance-preserving diffusion process traces. At fixed architecture and budget, switching the interpolant from VP to linear or generalized-VP is one of the two changes carrying SiT’s improvement over DiT, and it removes a singularity the VP interpolant has at one endpoint.
The logit-normal. This is the half that gets dropped in summary and should not be. In SD3’s ranking, rectified flow with uniform timesteps does not beat well-tuned epsilon-prediction; rectified flow with logit-normal timesteps does. That is a finding about SD3’s setting: latent text-to-image, against a tuned ε-prediction baseline. It is not a finding that uniform timesteps fail in general. The originating papers used uniform sampling and beat VP diffusion in pixel space. Flow Matching’s comparison is controlled (LIT-630 Table 1). Rectified Flow’s is partly controlled, because its training budget is unstated (LIT-636 Table 1a). At SD3’s scale the logit-normal decides the ranking. At small scale the path alone was enough. A reader training a large latent model should take both halves.
Where the advantage is largest
At few sampling steps. By 25 steps and above only the best-tuned
rectified-flow variant stays ahead of eps/linear; below that the gap is
wider. So the benefit lands where inference cost actually binds, which is a
better shape than a uniform improvement — it says when to bother.
Relation to what the record already holds
The logit-normal over t is the rectified-flow expression of what
SOTA-188 records in EDM’s coordinates: concentrate training where there is
something to learn, because the near-clean end is trivial and the
near-pure-noise end is nearly unlearnable. Two formulations, two coordinate
systems, one recommendation — and SOTA-188 had already listed Stable
Diffusion 3 as an implementation without the record holding the paper. The
listing was right, and now it has its reason.
SOTA-195 — predict v rather than the noise at low signal-to-noise — gets
independent support here too, from a different argument. That practice
reaches velocity prediction from the numerical failure of epsilon-prediction
near zero SNR; SiT reaches it from a clean ablation at fixed compute. Neither
knows about the other.
Why Active
Two groups, a controlled ablation and a broad sweep, a released 8B model and
released weights, nothing in the record contesting it, and a production
system built on it. The evidence is better than most of what this record
files as Active.
Conditions
No mechanism has been isolated. SiT offers reduced transport cost — the path length falls — and that is an observation accompanying the result, not an intervention separating it. An interpolant matched in path length but not straight would tell them apart and nobody has run it. So the whether is well established and the why is open. The closest anyone has come is a 2-D toy in Rectified Flow (LIT-636 Fig. 5), which runs VP with a linear α_t to separate path speed from curvature. It is qualitative. Rectified Flow’s straightness theorems apply to the reflowed coupling, not the single-pass model this practice recommends.
The 61-way sweep is at a smaller scale than the 8B run, which applies its winner rather than repeating it. SD3’s own scaling argument says that should be fine, and should be fine is what is established.
The image evidence is class-conditional ImageNet for the ablation and latent text-to-image for the scale run. The video evidence is one 5B ablation (LIT-626), judged by humans on 381 prompts. Its alignment margin is under twice the annotation σ that Movie Gen reports elsewhere. Nothing here is about the diffusion language models the record also holds (SOTA-157, SOTA-254), where the data is discrete and the straight-line construction does not obviously transfer.
The logit-normal is for training the base flow. A reflowed model’s hard cases are at the ends of [0, 1], not the middle, and Lee et al. (LIT-791) train the reflow stage with a U-shaped distribution, which beats uniform there (their Table 1); a logit-normal was not tried. Do not carry this half to reflow.
The logit-normal’s parameters are tuned, as EDM’s log-normal is. (0.00, 1.00) is what SD3 reports for the variant that stays competitive at higher
step counts, and it is a fit rather than a derivation.
Known implementations
- Stable Diffusion 3 (8B, weights released)
- SiT-XL
- Movie Gen, HunyuanVideo, Step-Video-T2V, Wan2.1 (video)