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REVIEW 3 major objections 5 minor 68 references

Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that a pre-trained diffusion model can be directly fine-tuned as a flow matching model by rescaling timesteps, aligning interpolants, and converting v-predictions into velocities, yielding faster convergence and better…

desk verdict Solid practical recipe for converting diffusion priors to flow matching, but the printed velocity conversion is algebraically wrong; the experiments suggest the code is right and the paper is wrong, so it needs a correction before acceptance. read the letter →

arxiv 2506.02221 v1 pith:4YSVEDLR submitted 2025-06-02 cs.CV cs.LG

Johannes Schusterbauer , Ming Gui , Frank Fundel , Björn Ommer This is my paper
classification cs.CVcs.LG
keywords diffusionmodelsflowmatchingfine-tuningLoRAparameter-efficientgenerativemodelingmonoculardepthestimationreflow
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

This paper tries to establish that the knowledge in a pre-trained diffusion model can be transferred to a flow matching model without retraining from scratch, by aligning the two paradigms' timesteps, interpolants, and prediction targets. If true, this would make flow matching's faster inference and straighter sampling trajectories available to the large installed base of diffusion checkpoints, while keeping training budgets small enough for parameter-efficient fine-tuning. The paper shows results on text-to-image synthesis, resolution change, reflow-based fast sampling, and monocular depth estimation, where the aligned objective converges faster than naively applying the flow matching loss and often beats continued diffusion training. The central move is to treat the diffusion trajectory and the flow matching trajectory as two coordinate systems on the same generative path, connected by invertible maps.

What carries the argument

The load-bearing object is the pair of invertible trajectory maps $(f_t, f_x)$ together with the velocity conversion formula. The timestep map $f_t$ sends the discrete diffusion timestep to the continuous flow matching time via the ratio $\alpha/(\alpha+\sigma)$, and the interpolant map $f_x$ rescales the diffusion sample by $1/(\alpha+\sigma)$ so the boundary points (clean data and noise) coincide. The velocity conversion takes the diffusion model's $v$-prediction, which mixes noise and data, and re-expresses it as the flow-matching velocity field, so the network does not have to unlearn its output parameterization. This is what carries the argument: it removes the 'unlearning' cost that makes naive FM fine-tuning slow and that breaks down under parameter-efficient fine-tuning.

What would settle it

The decisive check is algebraic: substitute the v-parameterization into the diffusion interpolant (Eqs. (3) and (8)) and solve for the estimated noise and data, then form the velocity $\hat{x}_0 - \hat{x}_T$ and compare with Eq. (16). A direct substitution gives $\hat{x}_T = \sigma x_t + \alpha v_\theta$ (not $\alpha v_\theta - \sigma x_t$), so the implied velocity is $(\alpha-\sigma)x_t - (\alpha+\sigma)v_\theta$ rather than $(\alpha-\sigma)(x_t - v_\theta)$; checking the released code against the printed equation settles whether the objective is the one the paper describes.

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Extended reading notes

Core claim

The central claim is that a v-parameterized diffusion model can be reused as a flow matching model by applying three coordinate changes: rescale the diffusion timestep by $f_t(\cdot)=\alpha/(\alpha+\sigma)$, rescale the noisy-sample interpolant by $f_x(\cdot)=x/(\alpha+\sigma)$, and convert the model's $v$-prediction into a velocity via the relation the paper derives as Eq. (16). With these changes, the standard flow matching loss $L_{\mathrm{FM}}$ is applied directly to the pre-trained diffusion network, with the inverse maps used during sampling to run Euler steps on the flow matching path. The paper reports that this alignment accelerates convergence relative to naive FM fine-tuning, that the advantage grows under LoRA-style parameter constraints, and that it extends to reflow training for low-step generation and to monocular depth estimation.

Load-bearing premise

The whole training target rests on Eq. (16), the formula that converts the diffusion model's v-prediction into a flow-matching velocity; if that conversion is algebraically wrong under the paper's own definitions, the fine-tuned model is trained to predict the wrong velocity.

Editorial extensions

If this is right

  • Directly fine-tuning a pre-trained diffusion model with the flow matching loss, without the proposed alignment, converges more slowly; with the alignment, competitive results appear in as few as 2.5k iterations in the paper's text-to-image experiments.
  • The alignment removes the zero-terminal-SNR artifact: the model can generate true black and white regions instead of gray, which the paper attributes to the rectified trajectories.
  • Reflow training becomes applicable to a diffusion prior: after one rectification pass, Stable Diffusion generates images with as few as 2-4 sampling steps without consistency distillation, using only a small fraction of tunable parameters.
  • For monocular depth estimation, the same recipe matches or improves on prior generative depth predictors with fewer training iterations, and LoRA with roughly a quarter of the parameters remains competitive with full fine-tuning.
  • Parameter-efficient fine-tuning with LoRA works when the alignment is used, but fails when the diffusion model is trained with a raw flow matching objective, because the model must learn an entirely new output parameterization.

Reading between the lines

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

  • Editorial extension: because the maps are bidirectional and require no extra parameters, the same conversion could be applied at inference time as a training-free wrapper, turning any off-the-shelf v-prediction diffusion checkpoint into a flow-style sampler; the paper presents the maps as part of fine-tuning, not as a standalone sampling trick.
  • Editorial extension: the paper's observation that non-integer diffusion timesteps with linearly interpolated noise schedules still produce high-quality images suggests diffusion timestep embeddings are effectively continuous; if that holds broadly, continuous-time diffusion sampling and schedule interpolation could be pushed further than the discrete training grid.
  • Editorial extension: the derivation is written for v-parameterization but the paper states it extends to epsilon-parameterization; if the same reasoning carries over, nearly any diffusion backbone could be converted to flow matching, which would broaden the transfer beyond image generation to video, audio, and dense prediction.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper proposes Diff2Flow, a method to convert a pre-trained diffusion model into a flow matching model by (i) rescaling timesteps via the signal-to-noise ratio, (ii) rescaling interpolants, and (iii) converting the diffusion model's v-prediction into an FM velocity estimate. The method is applied to text-to-image fine-tuning at a different resolution, to trajectory rectification (reflow) enabling 2-step generation, and to monocular depth estimation with PEFT (LoRA). The experimental results show faster convergence than naive FM fine-tuning and better performance than diffusion fine-tuning, especially under LoRA constraints.

Significance. The general goal of reusing established Stable Diffusion checkpoints for flow matching is timely and practically important. The paper contains extensive experiments across three tasks, including a reflow variant and depth estimation, and the observation that alignment-aware fine-tuning helps under parameter constraints is interesting. However, the central algebraic derivation of the velocity conversion in Eq. (16) is incorrect, which invalidates the method as described. The paper does not provide code to disambiguate whether the experiments used the printed formula or a corrected variant. If the derivation is fixed and the code confirms the corrected formula, the approach could be a valuable contribution; as written, the core claim is not supported.

major comments (3)
  1. [§3.2.2, Eqs. (15)–(16)] The velocity conversion is algebraically incorrect. Solving Eq. (8) and Eq. (14) for the clean and noise estimates gives x̂0 = (α x − σ v)/(α² + σ²) and x̂T = (σ x + α v)/(α² + σ²); the printed second line of Eq. (15), x̂T = α v − σ x, is therefore wrong, and the FM velocity x̂0 − x̂T equals (α − σ)x − (α + σ)v (for α² + σ² = 1), not (α − σ)(x − v) as in Eq. (16). This error changes the training target in Algorithm 1 and the sampling update in Algorithm 2; at α = σ the printed target is identically zero, which cannot produce a valid flow. Please provide the corrected formula and clarify whether the experiments were run with the printed formula or a corrected one, and make the code available to disambiguate.
  2. [§3.2.2, Eqs. (15)–(16)] The derivation implicitly assumes the variance-preserving condition α² + σ² = 1, but the paper also claims applicability to variance-exploding schedules (line after Eq. (8)) where α = 1 and σ varies. For VE schedules the inversion must divide by α² + σ² = 1 + σ²; as written, the formulas (even with corrected signs) would be wrong. Please either restrict the method to VP schedules or provide the general expressions.
  3. [§4 and Appendix A] The paper reports extensive experimental results but provides no code or model weights, and the algebraic error in Eq. (16) makes it impossible for a reader to determine whether the reported gains are due to the claimed alignment or to a different (possibly corrected) implementation. Given that the central formula is load-bearing, the authors should release the training and inference code, or at least specify the exact velocity conversion used in each experiment.
minor comments (5)
  1. [Eq. (15)] The notation dxDM_0 and dxDM_T with hats is confusing; I recommend using \hat{x}_0 and \hat{x}_T to denote the estimated clean and noise samples.
  2. [Figure 2] The caption states that non-integer-shifted DDIM timesteps produce high-quality images, but does not mention which model and schedule were used; please add this information.
  3. [Table 3] The CLIP scores of Diff2Flow at 25 steps are lower than SDv1.5+DPM Solver; the text describes the results as 'competitive' but this gap deserves a discussion, especially since FID is better.
  4. [§4.1] The claim that Diff2Flow solves the zero-terminal SNR issue is supported only by qualitative examples in Fig. 4; please consider adding a quantitative metric (e.g., average luminance of generated white/black images) to substantiate the claim.
  5. [Abstract and §3.3] Minor typos: 'na¨ıve' should be 'naïve' (or 'naive') in the abstract and elsewhere; 'contrain' in §3.3 should be 'constrain'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the alignment construction is definitional, the objective conversion is a derived (though possibly erroneous) algebraic step, and the empirical claims are tested against external benchmarks.

full rationale

The paper's derivation chain is self-contained rather than circular. The timestep and interpolant alignments in Eqs. (10)-(13) are explicit constructions: fx and ft are chosen so that the diffusion interpolant (8) maps onto the flow-matching interpolant (9), which is a definitional bridge and not a prediction smuggled from the result. The velocity conversion in Eqs. (15)-(16) is derived from the v-parameterization (3)/(14) and the interpolant (8); while the algebra appears questionable (solving the 2x2 system yields (alpha-sigma)x - (alpha+sigma)v rather than (alpha-sigma)(x-v), and at alpha=sigma the printed target becomes identically zero), this is a potential correctness error, not an equivalence-by-construction or a fitted parameter renamed as a prediction. The reflow experiments use image-noise pairs generated from the pretrained model itself following the standard Reflow procedure of Liu et al. [32], and the depth and text-to-image evaluations are compared against external benchmark numbers, including numbers reproduced by Martin Garcia et al. [38]; no load-bearing claim reduces to a self-citation. The paper's self-citations to DepthFM [14] and prior flow-matching work are used as baselines or related context, not as the justification for the method's central objective. Accordingly, no circular step meeting the evidence bar is present.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The method introduces no new physical entities or fitted constants. The mapping functions ft and fx are derived from the noise schedule; the velocity target is intended to be a deterministic function of the v-prediction. The main assumptions are standard diffusion-model accuracy assumptions plus the paper-specific hypothesis that non-integer timesteps are valid.

assumptions (4)
  • domain assumption The pretrained diffusion model's v-prediction is an accurate conditional estimator of v = α ε − σ x0, so the estimates in Eq. (15) are valid.
    Standard assumption in diffusion finetuning; the paper relies on it in Section 3.2.2.
  • standard math The timestep mapping ft(t) = α/(α+σ) is monotonic and invertible for the VP and VE schedules used.
    Follows from monotonicity of noise schedules; stated in Section 3.2.1.
  • ad hoc to paper Continuous timesteps between the discrete training timesteps behave like the discrete ones, because the sinusoidal timestep embedding creates a continuous space.
    Hypothesized in Section 3.2.1 and supported only by the qualitative Fig. 2.
  • domain assumption The reflow training pairs generated by ODE sampling from the pretrained model are valid targets for straightening the trajectory.
    Standard reflow assumption, Section 3.1 and 4.2.

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Cite this review

Pith. "Pith review of Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment." pith.science (2026). https://pith.science/paper/4YSVEDLR

@misc{pith2026250602221,
  author       = {Pith},
  title        = {Pith review of: Diff2Flow: Training Flow Matching Models via Diffusion Model Alignment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4YSVEDLR}},
  note         = {Machine review of arXiv:2506.02221}
}
read the original abstract

Diffusion models have revolutionized generative tasks through high-fidelity outputs, yet flow matching (FM) offers faster inference and empirical performance gains. However, current foundation FM models are computationally prohibitive for finetuning, while diffusion models like Stable Diffusion benefit from efficient architectures and ecosystem support. This work addresses the critical challenge of efficiently transferring knowledge from pre-trained diffusion models to flow matching. We propose Diff2Flow, a novel framework that systematically bridges diffusion and FM paradigms by rescaling timesteps, aligning interpolants, and deriving FM-compatible velocity fields from diffusion predictions. This alignment enables direct and efficient FM finetuning of diffusion priors with no extra computation overhead. Our experiments demonstrate that Diff2Flow outperforms na\"ive FM and diffusion finetuning particularly under parameter-efficient constraints, while achieving superior or competitive performance across diverse downstream tasks compared to state-of-the-art methods. We will release our code at https://github.com/CompVis/diff2flow.

Figures

Figures reproduced from arXiv: 2506.02221 by the authors.

Figure 1
Figure 1. We introduce a novel finetuning technique to traverse [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Although non-integer-shifted DDIM timesteps are nei [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Qualitative results for our finetuned Text-to-Image mod [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Our finetuning objective, both with and without PEFT [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Text-to-Image FID on the COCO 2017 [29] validation dataset. Light curves indicate results without Classifier-free Guidance [18]. a) We show that both FM and Diff2Flow converge to the same performance, given sufficient training and model capacity (full fine-tuning). How…
Figure 6
Figure 6. Figure 6: SD1.5 [46] + Diff2Flow-Reflow, 4-step inference results. Results [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 7
Figure 7. Figure 7: Zero-shot qualitative results on real-world imagery. Our methods produce depth predictions with perceptually higher fidelity and [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Results on NYUv2 depth benchmark [40] with 4 ensemble members. a) With full fine-tuning we find that FM adapts to the I2D task very quickly, but adding the objective change leads to even quicker convergence and better results. In contrast, the diffusion-based counterpa…
Figure 9
Figure 9. Figure 9: Diff2Flow enables fast monocular depth estimation with high fidelity. [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 10
Figure 10. Figure 10: 4-step inference results of our Diff2Flow-reflow model, using Stable Diffusion 1.5 as the prior diffusion model [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: 2-step inference results of our Diff2Flow-reflow model, using Stable Diffusion 1.5 as the prior diffusion model [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]
Figure 12
Figure 12. Figure 12: More qualitative results for monocular depth prediction compared to the state-of-the-art models (Part 1). [PITH_FULL_IMAGE:figures/full_fig_p015_12.png]
Figure 12
Figure 12. Figure 12: More qualitative results for monocular depth prediction compared to the state-of-the-art models (Part 2). [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: Qualitative results for monocular depth prediction. [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.