When does training on downscaled images yield the same gradients?

Seunghyun Ji

REVIEW 3 major objections 3 minor 14 references

When does training on downscaled images yield the same gradients?

T0 review · 3 major / 3 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that when training a diffusion transformer on downscaled latents, the gradient gap decomposes into a noise-dependent ratio term and a token-count floor, and that a measured map licenses selective low-resolution LoRA…

desk verdict Useful empirical study, but the route-uniformity claim at the heart of the two-term reduction conflicts with the paper's own Table 11. read the letter →

arxiv 2608.04448 v1 pith:6BD7J6EL submitted 2026-08-05 cs.CV cs.AI

Seunghyun Ji This is my paper · ORCID

classification cs.CVcs.AI

keywords diffusiontransformersflowmatchingdownscaledtraininggradientsimilarityLoRAtoken-countfloornoise-conditionalcosineattenuationcorrection

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Training a diffusion transformer on downscaled latents is cheap only if the downscaled step still produces the same gradient direction as the native step. The paper claims this question reduces to two separable effects: a noise-dependent term governed by the downscale ratio, which decays as the noise level rises, and a $\sigma$-independent floor set by the absolute token count of the target grid, which no amount of noise removes. With a debiased cosine estimator that removes finite-sample attenuation, the measured $(\text{route}, \sigma)$ map confirms this and finds a narrow window on the 1024 to 768 route that no spectral criterion predicts. Restricting LoRA training to the validated windows cuts training time by 14.6% at fixed steps while keeping the endpoint near the native retrain in weight space.

What carries the argument

The load-bearing object is the demotion distance $d_{e_0 \to e}(\sigma) = 1 - \cos(\bar{g}_{\mathrm{src}}(\sigma), \bar{g}_{\mathrm{dem}}(\sigma))$ between population mean adapter gradients, and the re-encoding excess $\mathrm{gap}_e(\sigma) = d_e(\sigma) - d_{\mathrm{reenc}}(\sigma)$ that subtracts the VAE round trip. The argument decomposes the perturbation $\delta g$ of the gradient $g = J^\top r$ into a data branch $\bar{J}^\top \Delta \bar{r}(\sigma)$, a graph branch $\Delta J^\top \bar{r}$, and a remainder, then reduces the cosine distance to a rotation-to-scale ratio $\kappa_{\mathrm{eff}}$ whose small-perturbation expansion yields a four-term form; assumptions (i) through (iv), including the route-uniformity of the residual mismatch, collapse it to the two-term reduction. The second key piece is the estimator: finite-draw cosine attenuation inflates distances more on coarser grids and manufactures the exact signature of a floor, so the paper applies Spearman's correction for attenuation via per-arm self-cosines and draw-limit extrapolation before any verdict is read.

What would settle it

Measure the cross-grid mean prediction-residual mismatch $\|\Delta \bar{r}(\sigma)\|$ at $\sigma = 1$ on the 1280 to 1120 iso-severity route with a draw count high enough to resolve 0.01, and compare it with the four-route family of Appendix Table 11; a deviation larger than the claimed $\pm 0.02$ band would jointly falsify assumption (iv) and the exponential-in-target-tokens floor law.

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Extended reading notes

Core claim

The paper's central claim is that a "demoted" training step, in which the native latent is replaced by a downscaled, re-encoded one, perturbs the adapter gradient through two structurally different channels. The first is a data branch set by the downscale ratio: its contribution to the gap is proportional to $\|\Delta \bar{r}(\sigma)\|^2 / \|\bar{g}_{\mathrm{src}}(\sigma)\|^2$ and decays as the noise level rises, just as the spectral premise predicts. The second is a graph branch that is independent of $\sigma$: it is set by the absolute token count of the target grid, carried partly by the rotary position embedding and partly by the coarse graph's residual capacity, and it cannot be removed by any noise level. The measured map shows 1024 to 896 is safe for $\sigma \in (0.5, 0.94]$, 1024 to 768 has a narrow low-excess window $0.65 < \sigma < 0.95$ that arises from negative data-graph interference, and any route to a 512-token grid is unsafe at every noise level. On this basis the paper claims a selective LoRA trainer saves 14.6% wall-clock at fixed steps while staying near-native in weight space.

Load-bearing premise

The whole two-term reduction leans on assumption (iv): the cross-grid prediction-residual mismatch has one universal $\sigma$-shape for every route, with route identity entering only as a scalar amplitude; the paper's own Table 11 shows spread up to about 0.075 at $\sigma = 1$, wider than the claimed $\pm 0.02$.

Editorial extensions

If this is right

On the paper's model, the spectral criterion "safe once noise masks the frequencies the coarse grid loses" is not a sufficient test for training; any low-resolution training proposal should be validated at the gradient level with a debiased estimator before being trusted.
The floor law implies that routes sharing the same target token count share the same $\sigma$-independent gap regardless of downscale ratio, so the cost of demotion is set by where you land, not by how far you shrink.
Gated demotion on the validated 1024 to 896 route at $\sigma > 0.5$ yields a 14.6% wall-clock saving at fixed steps with a weight-space endpoint within kernel-noise reach of native; late-scheduled demotion improves the endpoint cosine to about 0.75 with proportionally smaller savings.
The two-term reduction is not universal: the 1024 to 768 low-excess window is a signed failure of the reduction, caused by negative interference between data and graph branches, which the paper measures rather than explains away.
Held-out routes are predicted at about 0.07 to 0.09 RMSE from the ratio governor and an exponential-in-target-tokens floor law, compared with 0.147 to 0.355 RMSE for the spectral family.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the token-count floor is as universal as the paper's law suggests, even training schemes that restage the objective per resolution level carry an irreducible gradient-mismatch floor at coarse grids; output-level success in those schemes may come from the data term alone.
The debiasing result generalizes beyond this model: any comparison of gradients computed on different grid sizes or different draw budgets can manufacture a spurious floor, so cosine-attenuation correction should be standard in gradient-similarity audits.
A natural extension is to predict the map from a closed-form posterior covariance model rather than measuring the empirical mismatch curve; the paper shows second-order data-only closures recover the shape but not the amplitude, so the missing ingredient is likely caption-conditioned, non-Gaussian posterior structure.
The late-scheduled result suggests that scheduling demotion to late training is the most weight-preserving mode; testing whether the safe windows shift during the training trajectory is a direct next experiment.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

One thing to know before you read this paper: the central route-uniformity claim in §4.3 is contradicted by the paper's own Table 11, and the held-out predictions in Table 4 rest on that claim. The paper is still worth reading — the debiased estimator and the measured safety map are genuinely new — but the headline two-term reduction is not as well supported as the abstract implies.

What is actually new: this is the first gradient-level treatment of training on downscaled images for diffusion transformers. The estimand is carefully defined, and the paper builds a debiased cosine estimator using Spearman's attenuation correction, which addresses a real finite-draw artifact. The interventional data/graph split via a repromote arm is a nice piece of experiment design. The paper is also unusually explicit about margins, verdict resolution, and pre-registered criteria, and it ships code.

Soft spots, in order. First, §4.3 asserts the residual mismatch curve is 'the same for every route within ±0.02' and cites Table 11. The table actually shows spreads of about 0.037 at σ=0.125 and 0.075 at σ=1.0 across the four routes. That is not within ±0.02. Since the held-out predictions are produced by feeding one shared curve into Eq. 8, scaled only by per-route amplitude and floor, the route-transfer claim is stronger than the evidence. The held-out RMSE of 0.07–0.09 could in part reflect the fitted amplitude absorbing route-specific offsets rather than a confirmation of the decomposition. This is the main fix: re-run the predictive protocol with route-specific mismatch curves, or re-state the claim with error bars reflecting the observed spread.

Second, the two-term reduction does not predict the 768 mid-σ window, where the measured gap dips below the floor. The paper acknowledges this and traces it to negative interference, but it means the reduction's domain is narrower than the abstract suggests. Third, the floor 'law' is a two-anchor exponential fit, and the paper's own identifiability analysis shows other functional forms fit equally well. The limitations section says this, but the conclusion leans on it. Fourth, the training evidence is 480-step LoRA runs on two small corpora, so the 14.6% saving is suggestive, not generalizable. The single-model limitation is acknowledged.

Overall: the paper deserves a serious referee. It is well-written, honest about many limits, and the empirical map and estimator are real contributions. But the route-uniformity claim is load-bearing and contradicted by the paper's own numbers. I would accept it for peer review with major revision, requiring the route-specific re-analysis and re-scaled claims.

Referee Report

3 major / 3 minor

Summary. The paper asks whether a downscaled, re-encoded latent used during training preserves the native adapter gradient in a flow-matching DiT. It defines a population demotion distance, derives an exact angular identity (Eq. 6) and a four-term perturbation expansion (Eq. 7), reduces the excess gap to a two-term form (Eq. 8) under four assumptions, and proposes a debiased estimator for finite-draw attenuation. The measured per-route/per-sigma gap map is used to score a spectral account against a gradient-perturbation account, to validate the two-term reduction on two held-out routes, and to construct a sigma-gated LoRA trainer that reports 14.6% training-time savings at a fixed step budget.

Significance. The paper is unusually careful experimentally: it uses pre-registered gates, split-half reliability checks, deterministic kernels, paired draw sets, and a controlled two-adapter replication. The exact angular link (Eq. 6) and the branch decomposition (Eq. 5) are clean and self-contained, and the attempt to separate ratio-governed data effects from token-count-governed graph effects is valuable. If the route-uniformity assumption were supported, the held-out predictive RMSEs of 0.07–0.09 would be a strong result. However, the current evidence for route-uniformity conflicts with the paper's own Table 11, and the 1024→768 window is an acknowledged structural counterexample to Eq. 8, so the central claims need substantive revision before the paper can be accepted.

major comments (3)

[§4.3, Appendix Table 11, Assumption (iv), Eq. (8)] The claim that the residual mismatch curve is 'the same for every route within ±0.02' is contradicted by the table cited in its support. Table 11 reports relative-L2 cross-grid excess values with spreads of 0.037 at σ=0.125 (0.860–0.897), 0.064 at σ=0.375 (0.808–0.872), and 0.075 at σ=1.0 (0.360–0.435); at most sigma bins the spread exceeds 0.05. Because Eq. 8 consumes one shared ∥Δr(σ)∥ curve and scales it by a per-route amplitude a_e, a route-dependent mismatch shape can be absorbed by a_e and by the fitted floor, so the held-out RMSE values in Table 4 do not by themselves confirm the factorization. The held-out protocol should be re-run with route-specific mismatch curves, or the paper should provide a statistical test that the amplitude-times-shared-curve model is consistent with the residual-probe data within its stated precision.
[Eq. (8), §4.2, Appendix C] The 1024→768 mid-σ window is a structural counterexample to the two-term reduction, not merely a numerical miss. Eq. 8 is the sum of a nonnegative data term and a nonnegative floor, so it cannot produce a gap below the route's own floor; Table 6 shows paired excess values around +0.02 to +0.04 at σ=0.700–0.938 while the 768 floor is 0.06–0.09, and Appendix C confirms that 'a positive two-term reduction cannot produce a gap under its own floor.' Since the abstract and introduction present the reduction as the paper's central result, and §5 stacks this exact 768 window as a second training route, the central claim must be qualified to the domain in which assumptions (i)–(iv) hold, or the expansion must be extended to include the interference term. A limitation note is not sufficient when the flagship route is inside the reduction's failure region.
[§4.1–§4.2, abstract] The 'safe' verdicts for the 1024→896 and 1024→768 windows clear only the enlarged margin 0.09, not the strict margin ε=0.02 fixed at the outset of §4.1. The abstract says the downscaled gradient 'stays within a small margin of the native one' and §5 calls 1024→896 the 'measured-safe corpus route' without stating the margin; given the title's 'same gradients' framing, this is a material overstatement. The abstract and the safety claims should state the margin explicitly, and the practical training claims in §5 should be tied to the margin at which the route is actually certified.

minor comments (3)

[§4.3, Table 11] The text refers to route-uniformity across 'the three main routes' but the table contains four routes; clarify which routes enter the held-out protocol and which are simply descriptive, since 1280→1024 appears both in Table 11 and as a held-out route in Table 4.
[§5, Table 2] The pseudocode gates per-sample via 'if σ>σ* and y on-route', but the prose says 'When every sample in the batch is above the gate' the latent is replaced; specify whether mixed batches substitute per sample or are left entirely native, since this affects the reported wall-clock saving.
[§4.2, Fig. 1] The endpoint bin (σ=1) is plotted with open markers and later excluded from the safe interval σ∈(0.5,0.94], but this exclusion is stated only in the text; add the endpoint status and its margin explicitly to the figure caption.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: Eq. 8's inputs are measured and held-out predictions use zero per-route freedom.

full rationale

The derivation chain is not circular. Eq. 6 is an exact trigonometric identity (1 - cos(theta) = (1/2)||u-v||^2 for unit vectors), Eq. 7 is an algebraic expansion of Eq. 6, and Eq. 8 is explicitly conditional on four stated assumptions; the paper measures, rather than derives, the coefficients a_e, ||Delta rbar(sigma)||, ||gbar_src(sigma)||, and each route's floor. The predictive claims are tested on held-out routes with zero per-route freedom (Appendix C): amplitudes and floors come from the ratio governor and the token-count floor law fitted only on fit routes {1024->896, 1024->512, 1280->1120}, and the held-out routes {1024->768, 1280->1024} are not used in those fits. The comparison against the spectral account and an oracle quadratic fit on the held-out data itself provides an external benchmark. The paper's own limitations are explicit and located: Section 6 concedes that the floor law's functional form is unidentified at the operating points and that 1280-tier curves remain pre-debiasing reads, and Appendix B quantifies the identifiability limits. The one substantive empirical discrepancy, the 'within +/-0.02' route-uniformity claim versus Appendix Table 11's spreads of about 0.037 at sigma=0.125 and 0.075 at sigma=1.0, weakens the support for assumption (iv), but it is a correctness and robustness concern, not a circularity: Eq. 8 is not equal to its inputs by construction, and the held-out predictions do not simply rename fitted values. No load-bearing step reduces by definition or by self-citation to its own inputs, so the appropriate finding is no significant circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The exact angular and branch algebra is self-contained, but the reduction to Eq.8 pulls in three fitted or measured ingredients: per-route amplitude a_e, the measured residual mismatch curve, and the exponential floor law. Assumptions (iii) and (iv) are tested but partly fail or are under-supported, so the 'two-term reduction' is an empirical decomposition with a small amount of fitted structure.

free parameters (3)

route amplitude a_e = not tabulated; fit per route (Table 3 leg amplitudes 0.05-1.09 in units of ||g_src||)
Eq. 8's data term multiplies the measured residual-mismatch norm by a_e. Appendix A.4 states the loading is an empirical ingredient, fit and tested held-out, not derived.
exponential floor law constants F0, tau = F0=0.70, tau=1041 tokens (Appendix C; tau range 860-1040)
Fit to endpoint floors at 512 and 896 target tokens and used to predict 768; the paper says the functional form is unidentified, so 'token-count law' is a two-anchor fit.
ratio governor A(ratio) = not quantified; interpolates between ratio 0.875 and 0.75 route amplitudes
Held-out data-term amplitudes come from interpolating measured amplitudes over two ratio values; two points support the governor.

assumptions (5)

domain assumption Cross-grid branch split requires a fixed identification of source and demoted output spaces; only the total delta_g is identification-independent.
Appendix A.2. The two-term reduction treats the operational B/C/R split as meaningful.
domain assumption Assumption (iii): graph share Phi_e is sigma-stationary.
§3.4; endpoint floors measured at sigma=1 are read across the high-sigma plateau.
domain assumption Assumption (iv): data-branch factorization with route-uniform mismatch, claimed within ±0.02.
§3.4; Appendix Table 11 shows spreads above this and Appendix A.4 admits the loading is empirical.
domain assumption The trained-model residual mismatch curve is the minimal honest closure of the posterior operator (no structured Gaussian closure passes).
Appendix A.3; the account consumes the measured curve as-is.
domain assumption At sigma=1 and x-zero, the measured gap isolates the graph branch; target-mediated perturbation lands parallel to native gradient.
§4.3 and Appendix B; the alpha-flat result is required for the endpoint floor read.

invented entities (1)

Graph floor Phi_e = RoPE_e + Resid_e independent evidence
purpose: Sigma-independent gap component set by target token count
Defined from Eq.8 and measured with sigma=1 and x-zero probes; positional-interpolation erases the RoPE share, leaving Resid. It is a measured decomposition, not a postulated hidden cause.

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Cite this review

Pith. "Pith review of When does training on downscaled images yield the same gradients?." pith.science (2026). https://pith.science/paper/6BD7J6EL

@misc{pith2026260804448,
  author       = {Pith},
  title        = {Pith review of: When does training on downscaled images yield the same gradients?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6BD7J6EL}},
  note         = {Machine review of arXiv:2608.04448}
}

read the original abstract

Diffusion transformers deliver strong image generation, but their training cost grows superlinearly with resolution. Recent work justifies training or sampling at reduced resolution on a spectral premise: at high noise, a downscaled latent preserves almost the full surviving signal. Whether a downscaled step also preserves the native training gradient signal, however, has remained unresolved. We reduce how that signal changes under downscaling to two terms: a noise-dependent term governed by the downscale ratio, which decays at high noise as the spectral premise predicts, and a \sigma-independent floor governed by the target grid's absolute token count, carried by the compute graph itself and removed by no noise level. The measured (route, \sigma) map corroborates the account and uncovers structure the spectral picture cannot express: on the 1024->768 route, a window (0.65 < \sigma < 0.95), predicted by no spectral criterion at any tolerance, where the downscaled gradient stays within a small margin of the native one. Training LoRA adapters with downscaled steps restricted to the routes and noise windows the map validates reduces training time by 14.6% at a fixed step budget while remaining near-native in weight space. Code is available at https://github.com/sorryhyun/anima_lora.

Figures

Figures reproduced from arXiv: 2608.04448 by the authors.

**Figure 1.** The measured map, and both accounts on the same axes. Per route, one set of measured debiased gap curves (Eq. 1, black; open markers detach the 𝜎=1 endpoint bin, a distinct probe mode) carries the verdict of §4.2, read per bin against the gray band, the bin-level ±𝜀 ∗ verdict resolution (§4.1). The same axes carry both predictions of §3: the spectral account (red dashed), transported through the residual→gradient br… view at source ↗

**Figure 2.** Visual counterpart to Table 1: matched (prompt, noise-seed) renders from the arms’ [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** The second held-out route, 1280→1024, under all three functional forms for the data term of Appendix C (fitted power, derived quadratic, exact angular link; legend 𝐺 := ∥𝑔¯src (𝜎) ∥), predicted from governors fitted on other routes. This is the one route where the forms visibly separate: the derived quadratic systematically overshoots the mid-𝜎 peak; the exact angular link’s saturation removes the overshoot (RMSE 0.… view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: The ledger’s geometry. Left: the three arms as corners of the data–graph lattice. 𝐵 and 𝐶 are the partial differences along the lattice’s only realizable path — the fourth corner (native content on the coarse graph) does not exist — so the split is a round trip off the…

**Figure 5.** Figure 5: The spectral account, computed from the measured RAPSD and transported to the training [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]

**Figure 6.** Figure 6: The whole tolerance family against the measurement: the detail behind the single red curve of [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]

**Figure 7.** Figure 7: The Fig. 8a recipe repeated on two controlled adapters trained on opposite style clusters, [PITH_FULL_IMAGE:figures/full_fig_p026_7.png]

**Figure 8.** Figure 8: The measurement in detail. (a) Debiased demotion gap per [PITH_FULL_IMAGE:figures/full_fig_p027_8.png]

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Works this paper leans on

14 extracted references · 8 canonical work pages

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gap 768 within the re-encoding band at𝜎≥0.5

Left three panels: the measured debiased gap curves against the spectral account transported through our bridge (the diagonal model’s destroyed-band mean-residual mismatch on the measured spectrum, through the measured∥¯𝑔 src(𝜎)∥with a single gain calibrated on the one safe route and no floor, which the family cannot express), gated at𝑡 ∗(𝛿)(dashed vertic...

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5): predicted safe boundaries𝑡 ∗ per route as the tolerance𝛿sweeps its range.𝛿 reenc is the measured re-encode noise floor, a zero-free-parameter anchor fixed by our own pipeline

instantiated on the measured latent spectrum (𝑃at the 896/768/512 cuts=0.025/0.029/0.065; RAPSD in Fig. 5): predicted safe boundaries𝑡 ∗ per route as the tolerance𝛿sweeps its range.𝛿 reenc is the measured re-encode noise floor, a zero-free-parameter anchor fixed by our own pipeline. No row reproduces the measured pattern (last line): the𝛿that matches the ...

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The floor law’s identifiability.Two anchors and one held-out check cannot identify a functional form, and the cosine gap is the wrong scale to fit one in: it saturates (Eq. 6). Refitting the same anchors in the unsaturated perturbation-energy units𝜅 2 eff =(1−𝐹) −2−1 gives𝜏≈860 tokens and predicts𝐹(2160)=+0.096, equally consistent with the measured+0.092±...

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this admits exactly two mechanisms, both pre-registered ahead of the probe: either the projected interaction is negative in the window (𝐼 768 <0, in which case amplitude matching predicts the window center sits where the two perturbation legs have equal orthogonal magnitude, a testable localization), or the graph share is itself𝜎-dependent, rewriting assu...

work page 2026
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6), both withzero per-route freedomon held-out routes: amplitudes and floors come from the two governors of§4.3 fitted on{1024→896,1024→512,1280→1120}

and the exact angular link (Eq. 6), both withzero per-route freedomon held-out routes: amplitudes and floors come from the two governors of§4.3 fitted on{1024→896,1024→512,1280→1120}. The oracle is a quadratic-in-𝜎fit on the held-out data itself, the noise ceiling for a 3-dof curve, so beating it on 1024→768 means the prediction is at the data’s own resol...

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

gap 768 within the re-encoding band at𝜎≥0.5

Left three panels: the measured debiased gap curves against the spectral account transported through our bridge (the diagonal model’s destroyed-band mean-residual mismatch on the measured spectrum, through the measured∥¯𝑔 src(𝜎)∥with a single gain calibrated on the one safe route and no floor, which the family cannot express), gated at𝑡 ∗(𝛿)(dashed vertic...

work page 2026

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Spectrally-guided diffusion noise schedules.arXiv preprint arXiv:2603.19222,

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arXiv

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5): predicted safe boundaries𝑡 ∗ per route as the tolerance𝛿sweeps its range.𝛿 reenc is the measured re-encode noise floor, a zero-free-parameter anchor fixed by our own pipeline

instantiated on the measured latent spectrum (𝑃at the 896/768/512 cuts=0.025/0.029/0.065; RAPSD in Fig. 5): predicted safe boundaries𝑡 ∗ per route as the tolerance𝛿sweeps its range.𝛿 reenc is the measured re-encode noise floor, a zero-free-parameter anchor fixed by our own pipeline. No row reproduces the measured pattern (last line): the𝛿that matches the ...

work page 2026

[4] [6]

The floor law’s identifiability.Two anchors and one held-out check cannot identify a functional form, and the cosine gap is the wrong scale to fit one in: it saturates (Eq. 6). Refitting the same anchors in the unsaturated perturbation-energy units𝜅 2 eff =(1−𝐹) −2−1 gives𝜏≈860 tokens and predicts𝐹(2160)=+0.096, equally consistent with the measured+0.092±...

work page 2025

[5] [7]

this admits exactly two mechanisms, both pre-registered ahead of the probe: either the projected interaction is negative in the window (𝐼 768 <0, in which case amplitude matching predicts the window center sits where the two perturbation legs have equal orthogonal magnitude, a testable localization), or the graph share is itself𝜎-dependent, rewriting assu...

work page 2026

[6] [8]

6), both withzero per-route freedomon held-out routes: amplitudes and floors come from the two governors of§4.3 fitted on{1024→896,1024→512,1280→1120}

and the exact angular link (Eq. 6), both withzero per-route freedomon held-out routes: amplitudes and floors come from the two governors of§4.3 fitted on{1024→896,1024→512,1280→1120}. The oracle is a quadratic-in-𝜎fit on the held-out data itself, the noise ceiling for a 3-dof curve, so beating it on 1024→768 means the prediction is at the data’s own resol...

work page arXiv

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Uncertainty in a Single Pass: A Closed-Form Identity for One-Step Flow Matching

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work page Pith review arXiv

[8] [1904]

Scale-wise distillation of diffusion models.arXiv preprint arXiv:2503.16397,

Nikita Starodubcev, Ilya Drobyshevskiy, Denis Kuznedelev, Artem Babenko, and Dmitry Baranchuk. Scale-wise distillation of diffusion models.arXiv preprint arXiv:2503.16397,

arXiv