Title: CAR-Flow: Condition-Aware Reparameterization Aligns Source and Target for Better Flow Matching
Venue: NeurIPS 2025
Accepted: yes
Keywords: image generation

diffusion model

flow matching
Abstract: Conditional generative modeling aims to learn a conditional data distribution from samples containing data-condition pairs. For this, diffusion and flow-based methods have attained compelling results. These methods use a learned (flow) model to transport an initial standard Gaussian noise that ignores the condition to the conditional data distribution. The model is hence required to learn both mass transport \emph{and} conditional injection. To ease the demand on the model, we propose \emph{Condition-Aware Reparameterization for Flow Matching} (CAR-Flow) -- a lightweight, learned \emph{shift} that conditions the source, the target, or both distributions. By relocating these distributions, CAR-Flow shortens the probability path the model must learn, leading to faster training in practice. On low-dimensional synthetic data, we visualize and quantify the effects of CAR-Flow. On higher-dimensional natural image data (ImageNet-256), equipping SiT-XL/2 with CAR-Flow reduces FID from 2.07 to 1.68, while introducing less than \(0.6\%\) additional parameters.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis work introduces CAR, a technique to improve conditional flow matching models by learning a transformation of the latent and/or data distribution that depends on the condition. The flow matching model is then applied to map between these two transformed distributions. More specifically, the authors first identify five classes of degenerate zero-cost solutions of flow matching that can be achieved when using arbitrary transformations. They then notice that it is impossible to create these solutions with only a shift of both distributions, and thus propose to include a learned shift before and after the mapping induced by flow matching. They then verify in a toy example that the proposed shift transformation learns a non-degenerate solution, whereas including scaling also leads to one of the zero-cost solutions in practice. Finally, they demonstrate that even this simple addition to the FM framework yields significant improvements on conditional ImageNet 256x256.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths**  \n- The presented method is simple and seems applicable to most conditional flow matching scenarios\n- The results achieved on ImageNet 256x256 are very convincing\n- The identified trivial minima are not only relevant for this work but might help to illuminate problems that occur in adjacent work which performs joint training of flow matching and pre-/post-hoc transformations.\n- The method is very lightweight and seems to have almost no implementational and computational overhead  \n- The writing is very clear, proofs are formulated understandably and the toy example is quite instructive.\n\n**Weaknesses**\n- The method's quantitative and qualitative performance was only compared against baseline flow matching on a single dataset. While the results are convincing there is still room to explore how it performs for different dataset and condition types\n- The improvements in convergence speed were only shown for the 1-d toy example. It would be interesting to see if improved convergence speed is also observed on high-dimensional data.\n- The authors only consider the simplest transformation that avoids the identified trivial solutions. More complex transformations might result in much better performance \n\nMinor things:\n- The qualitative results in the appendix lack a baseline comparison\n- The shift prediction network learning rate needs to be fine-tuned to see the beneficial effects of CAR (but according to Fig. 6 it seems very lenient)\n\nIn conclusion, while the extent of performance gain that can be expected from CAR (and possibly more advanced versions) might not be quantified entirely from the limited experiments in this paper, due to the mentioned strengths it can be expected to overall contribute positively to CFM training.\n\nQUESTIONS:\n- Do you have a notion of how complete the list of failure modes in Claim 1 is? Are there other problems beyond mode collapse that could occur?\n- Have you tried to apply CAR for continuous conditions? Can you observe similar benefits?\n- Have you tried more general transformations (e.g. volume-preserving transformations would seem to avoid all the trivial solutions as well)?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-20"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes CAR, condition-aware reparametrization, a technique to train source and target transformations simultaniously with the velocity field in the flow matching frameworks. This approach allocates some capacity for processing the conditioning separately from the main flow matching objective, which fosters the alignment between the source and the target distributions, and thereby eases the optimization of the velocity field. The authors provide theoretical analysis of the degenerate solutions in the general unresticted settings and derive the shift-only CAR to avoid those. Experiments on synthetic and real-world data support the claims made in the paper and demonstrate superior performance compared to the prior work.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n1. The paper is well-written and the motivation is clear. The method is simple and theoretical foundations are provided. The results on both synthetic and real data support the claims made in the paper.\n\n### Weaknesses\n\n1. The main weakness of the paper is the lack of clarity in delivering the theoretical results. It is not clear why the degenerate 0-cost solutions are presented as \"$\\theta$-independent\". These are analytical solutions that exist in the general setting, but if the $\\theta$-depended model converged to these during the optimization process they still depend on parameters. \n2. The proportional collapse case is unclear. In the loss (equation 9), $x_0$ and $x_1$ are sampled independently from each other. However, case *(v)* somehow suggests that $z_0$ and $z_1$ are coupled. Could the authors clarify this?\n3. The unbounded case also requires further clarifications. In general, the 0-cost solution of the optimization problem in equation 9 is feasible if the are no intersections between the trajectories that interpolate $z_0$ and $z_1$. While in cases *(i)* and *(ii)* this is clear, in the case where both the target and the source distributions have non-trivial supports, there will be intersections, unless the source and the target are non-trivially coupled. I would like to see more discussion of this issue in the cases *(iii)-(v)*.\n\nQUESTIONS:\n1. While the method is motivated for the conditional case, I think the unconditional generation can also benefit from the proposed source/target alignment. Could the authors provide any insights on why the proposed approach should/sould not work for the unconditional setting?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors in this paper propose Condition-Aware Reparameterization (CAR) as a method for imprving conditional generative models especially in diffusion and flow-matching frameworks. Standard conditional generation methods rely on a standard Gaussian prior, forcing the model to handle both semantic conditioning and distribution matching, leading to inefficient, long probability paths during training. Proposed method mitigates this by shifting the source and/or target distributions in a condition-aware manner aligning distributions to reduce the burden on the main model. The authors provide theoretical analysis demonstrating that unrestricted reparameterizations can cause mode collapse. By restricting to additive shifts only, CAR avoids these trivial minima while maintaining benefits in path shortening. Experiments on synthetic data and ImageNet-256 show that CAR consistently improves convergence speed and sample fidelity.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n1. The paper proposes an interesting solution for reducing the complexity of conditional flow matching by aligning distributions via learnable shifts.\n2. The theoretical analysis of the paper is well complimented by empirical analysis.\n3. CAR is easy to integrate into existing frameworks, adding minimal overhead, and provides consistent improvements in convergence and sample quality.\n\nWeaknesses:\n1. The method is currently limited to shift-only reparameterizations.\n2. Detailed ablation study should be performed to quantify contribution of various components.\n3. Empirical validation focuses on FID and ImageNet; more diverse datasets and modalities (e.g., text, audio) are not explored.\n4. How CAR works for models such as FFJORD or neural autoregressive flows is yet to be covered. (Grathwohl, Will, et al. \"Ffjord: Free-form continuous dynamics for scalable reversible generative models.\" arXiv preprint arXiv:1810.01367 (2018)., Huang, Chin-Wei, et al. \"Neural autoregressive flows.\" International conference on machine learning. PMLR, 2018.)\n\nQUESTIONS:\n1. How does CAR perform when conditioning signals are noisy or weak?\n2. Have you explored combining CAR with various transformations under constraints?\n3.Can you discuss how this will extend to models like FFJORD or neural autoregressive flows?\n4.Some ablation study results will be appreciated.\n5. Can CAR be extended to multi-modal or multi-task settings?\n\nLIMITATIONS:\nThe authors can discuss the limitations in some more detail, covering multi modal modeling, more flow models especially like FFJORD and neural autoregressive flows, cases when conditioning signal is weak, transformation under constraints, etc.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 3, "IMPACT": 4, "ORIGINALITY": 3, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\n* The paper introduces Condition-Aware Reparameterization (CAR) which is a new way of doing conditional generative modeling. CAR explicitly incorporates conditioning information into generative models via learned, shift-only reparameterizations of either the source or target distributions. This simplifies the training of flow-based generative models and enhances their sampling efficiency.\n\n* The authors provide theoretical insights, demonstrating that allowing certain families of reparameterizations can lead to degenerate, trivial solutions. By restricting reparameterizations to shift-only transformations, CAR avoids these degenerate cases.\n\n* In the synthetic dataset example, trajectory lengths being shorter does not necessarily imply that generation quality improves. Indeed, the CAR method can be seen as decomposing the trajectory into different stages x_0 -> z_0 -> z_1 -> x_1, so naturally the length of the z_0 -> z_1 path would be shorter. However, by measuring the Wasserstein divergence of the generated distribution and the ground truth, the authors verify that the quality of the generated samples is better when using CAR.\n\n* Empirical validation shows CAR reduces trajectory lengths and improves sampling quality. Specifically, it achieves gains on ImageNet generation benchmarks (e.g., improving FID from 2.07 to 1.68 on ImageNet-256) with minimal additional parameters.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n* The authors do a good gob laying out the foundations and formalizing their framework. The presentation overall is mostly clear.\n* The paper provides both a simple demonstration of their proposed algorithm (CAR) on synthetic dataset. This is useful to understand that CAR reduces the trajectory length in latent space, potentially leading to less error due to discretization. On the other hand, the authors also show that CAR improves FID performance on ImageNet, which is evidence of the practical use of this method.\n\nWeaknesses\n* Although the theoretical claims (Claim 1 and Claim 2) are interesting, they are mostly characterizing degenerate behavior. This leaves the reader without a sense of what are optimal \\mu_0 and \\mu_1 in non-degenerate cases. Understanding theoretically the case where the target is a two-class Gaussian mixture would be ineresting. If that is too hard, a simplification would be to understand the optimal \\mu_0 for the case where the target is a symmetric sum of diracs (which I believe doesn’t match the triviality conditions from Claim 1)\n* It is known in the literature that changing the source distribution can lead to lower transport costs (e.g. Albergo and Vanden-Eijnden 2023). Instead of learning a distribution for the y, we could just learn a distribution for the x_0 instead of  using the N(0, Id). Note that there are ways of doing this using only a few parameters like still parameterizing x_0 by a Gaussian, but learning the mean and covariance (where we could assume the covariance is diagonal if we want to save parameters.) Although this wouldn’t decouple “transporting mass” and “encoding semantics”, it is not clear that this is needed, and having a learnable distribution for x_0 may already explain the performance increase.\n\nQUESTIONS:\n* Do you have any examples (theoretical or empirical) where learning the distribution for y performs better than just learning it for x_0? (also see first weakness above)\n* You mention that your method decouples the “transporting mass” and “encoding semantics.” However, I don’t see any reason for it being problematic to learn these two behaviors at the same time. Is there any intuition you could provide for what you have in mind here?\n* Do you have any intuition on why the target-only CAR leads to paths with smaller lengths and lower FIDs than the source-only CAR?\n* The meaning of cases (iii) and (iv) is not very clear from what is written in Claim 1.\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 2, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-03"}