Title: Single-Step Diffusion via Direct Models
Venue: NeurIPS 2025
Accepted: no
Keywords: Efficient generative models
Abstract: We introduce Direct Models, a generative modeling framework that enables single-step diffusion by learning a direct mapping from initial noise $x_0$ to all intermediate latent states along the generative trajectory. Unlike traditional diffusion models that rely on iterative denoising or integration, Direct Models leverages a progressive learning scheme where the mapping from $x_0$ to $x_{t + \delta t}$ is composed as an update from $x_0$ to $x_t$ plus the velocity at time $t$. This formulation allows the model to learn the entire trajectory in a recursive, data-consistent manner while maintaining computational efficiency. At inference, the full generative path can be obtained in a single forward pass. Experimentally, we show that Direct Models achieves state-of-the-art sample quality among single-step diffusion methods while significantly reducing inference time.

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Abstract

We introduce Direct Models, a generative modeling framework that enables singlestep diffusion by learning a direct mapping from initial noise x 0 to all intermediate latent states along the generative trajectory. Unlike traditional diffusion models that rely on iterative denoising or integration, Direct Models leverages a progressive learning scheme where the mapping from x 0 to x t + δt is composed as an update from x 0 to x t plus the velocity at time t . This formulation allows the model to learn the entire trajectory in a recursive, data-consistent manner while maintaining computational efficiency. At inference, the full generative path can be obtained in a single forward pass. Experimentally, we show that Direct Models achieves stateof-the-art sample quality among single-step diffusion methods while significantly reducing inference time.

1 Introduction

Diffusion models and flow matching methods have recently achieved remarkable success across a wide range of applications, including image synthesis [5], audio generation [7], and 3D shape modeling [10]. Despite their effectiveness, a significant limitation of these approaches lies in their reliance on iterative sampling or inference procedures, which are computationally expensive and can limit real-time deployment.

To address this bottleneck, some recent works have explored distillation techniques to compress multi-step diffusion or flow matching models into efficient single-step samplers. Notable examples include [12, 16], which require first training a high-quality teacher model and then performing a costly distillation step. Moreover, such distillation sometimes involves constructing large synthetic datasets, increasing the complexity and resource demands of the overall pipeline.

In contrast, this work proposes a novel single-run training approach that directly learns a one-step diffusion-like generative model without relying on teacher models or distillation. Our method offers a more practical and efficient solution for fast sampling, avoiding the overhead inherent in multi-stage training pipelines and results in high-quality samples (see Figure 1).

To address these challenges, we propose a new class of Direct Models , a residual-based formulation that enables both single-step sampling and single-run training. The key idea is to directly model the full flow map through a time-indexed residual field, allowing us to query any intermediate latent x t without requiring numerical integration. This direct access to latents motivates the name of our approach.

At the core of our method lies a simple recursive structure: the residual displacement at time t + δt is 32 expressed as a combination of the residual at time t and the local velocity at that point. This recursive 33 formulation not only serves as a training objective but also acts as a structural prior, encouraging 34 consistency across time steps while remaining efficient and fully self-supervised. 35

Our main contributions are as follows: 36

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We propose Direct Models, a novel direct residual model for one-step flow generation that enables efficient single-step sampling without iterative inference.

We introduce a recursive training framework, based on a straightforward mathematical derivation based on a Taylor expansion of the flow, that enforces local velocity consistency, allowing the model to be trained in a single run.

We demonstrate that Direct Models achieves superior sample quality compared to existing single-step, single-run generative approaches, closing the gap with iterative methods while maintaining fast inference.

2 Preliminaries: Continuous-Time Generative Models 45

Modern generative modeling has been significantly shaped by methods that transform simple source 46 distributions into complex data distributions through continuous-time dynamics. Two prominent 47 families in this space are diffusion-based models ( e . g ., [18, 5, 19]) and flow-based approaches , 48 particularly those based on flow matching [8, 9]. These frameworks parameterize sample trajectories 49 using neural differential equations, typically in the form of an ODE, to transport mass smoothly from 50 a source distribution ( e . g ., Gaussian noise) to a target data distribution. 51

In this work, we adopt a flow matching viewpoint, leveraging its optimal transport-inspired formu52 lation to model deterministic sample paths. Notably, recent studies ( e . g ., [6]) have emphasized the 53 close relationship between diffusion and flow-based models, observing that flow matching can be 54 viewed as a deterministic instance of more general stochastic diffusion processes. As such, we view 55 these paradigms as conceptually intertwined and refer to them in parallel where appropriate. 56

Formally, consider a pair of distributions: a base distribution µ 0 and a target distribution µ 1 . The 57 goal is to learn a velocity field v θ ( x, t ) , parameterized by a neural network, that defines the evolution 58 of a sample over time 59

Solving this ODE from t = 0 to t = 1 generates a trajectory that ideally maps µ 0 into µ 1 . 60

A practical and efficient instantiation of this idea is given by Conditional Flow Matching (CFM) , 61 which sidesteps density estimation by using known correspondence pairs ( x 0 , x 1 ) ∼ ( µ 0 , µ 1 ) . Rather 62 than relying on stochastic score-based gradients, the model is trained to approximate the ground-truth 63 transport velocity along straight-line paths 64

The true instantaneous velocity along this path is simply x 1 -x 0 , and the model v θ ( x, t ) is trained 65 to match this velocity using the loss 66

This supervised objective encourages the model to replicate the optimal displacement between samples 67 at intermediate points in time, by constructing a continuous flow without requiring likelihoods or 68 sampling noise. Once trained, generation consists of drawing x 0 ∼ µ 0 and integrating the ODE (1) 69 forward using the learned dynamics. This process can be efficiently implemented with standard ODE 70 solvers such as Euler or Runge-Kutta methods. 71

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3 Method: One-Step Flow via Direct Models

3.1 Formulation

We introduce a one-step generative model by directly parameterizing the flow map ϕ ( x, t ) . A natural 74 formulation is to define the flow as ϕ ( x, t ) = x + w ( x, t ) , where the residual field w ( x, t ) captures the 75 displacement from the initial point. However, this choice allows the magnitude of the displacement to 76 vary arbitrarily with time which we found leading to unstable training. To impose a form of temporal 77 consistency, we instead define the flow as 78

where w ( x, t ) ∈ R d is now interpreted as a normalized direction of displacement , and the scaling 79 by t ensures that the overall displacement grows smoothly from zero to its final value. This parame80 terization encourages the magnitude ∥ t · w ( x, t ) ∥ to vary linearly with time, providing a stable and 81 interpretable structure for learning. This formulation provides a single-step trajectory, in contrast to 82 the continuous ODE integration approach commonly used in flow matching. 83

In the flow matching framework, the temporal derivative of the trajectory satisfies 84

where v ( x t , t ) is the target velocity field at the point x t = ϕ ( x, t ) . To incorporate this into our model, 85 we compute the time derivative of ϕ ( x, t ) as defined in Equation (4) 86

We approximate the time derivative of w ( x, t ) using the forward difference with a discrete δt step 87

By substituting this approximation into the derivative of ϕ ( x, t ) , we obtain 88

By matching this expression to the target velocity v ( x t , t ) , we then have 89

which can be rearranged into the equation 90

Finally, by multiplying both sides by δt t we have 91

and by isolating w ( x, t + δt ) , we arrive at 92

3.2 Training Direct Models via Local Velocity Propagation 93

To learn the flow map parameterized by a model w ν , with parameters ν , we leverage the recursive 94 structure implied by the progressive velocity propagation equation 95

.

This relation connects the residual field w at two consecutive time steps through the velocity field v 96 We exploit this property to define a consistency-based training loss for w ν , encouraging it to align 97 with the propagated velocity information. 98

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In our formulation, we train two models jointly:

v θ ( x, t ) : a velocity field trained using the standard Conditional Flow Matching (CFM) loss,

w ν ( x, t ) : a residual displacement field trained using a recursive propagation loss derived from Equation (13).

The velocity field v θ is trained using the standard Conditional Flow Matching (CFM) loss. Given a sample pair ( x 0 , x 1 ) ∼ ( µ 0 , µ 1 ) and a uniformly sampled time t ∼ U [0 , 1] , we define the intermediate point

The CFM objective encourages the predicted velocity to match the ground-truth displacement between x 0 and x 1 at this intermediate point

The residual field w ν is trained using a local velocity propagation loss derived from Equation (13). Given the sample x 0 ∼ µ 0 , a small step size δt and t ′ ∼ U [ δt, 1 -δt ] , we define the propagation loss as

with x ′ t = x 0 + t ′ · sg [ w ν ( x 0 , t ′ )] , where sg [ · ] denotes a stop-gradient operator. Notice that we define the residual field model w ν only with respect to the samples x 0 from the initial distribution µ 0 . In this way, at inference we can directly map these samples to any point along the trajectory in one step, and, in particular, to the target distribution samples x 1 . Although w ν ( x 0 , t ′ ) may be initially uninformative at the beginning of the training, the propagation loss remains effective, removing the need for explicit scheduling of t ′ . This simplifies training, improving stability and practicality without compromising performance.

Our training algorithm is outlined in Algorithm 1.

3.3 Sampling from Direct Models

Sampling from our direct flow map model is straightforward and efficient. Given an initial sample x 0 ∼ µ 0 , the corresponding transformed sample x 1 can be obtained via a single forward pass of the residual field

This one-step sampling eliminates the need for iterative procedures, making the approach practical and fast for inference.

4 Experiments

4.1 Settings

In this section, we compare our method against several existing approaches. All models are trained 127 from scratch using the same architecture and implementation framework to ensure a fair comparison. 128

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Specifically, we adopt the DiT-B diffusion transformer architecture from [14].

Our experiments

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Algorithm 1 Training Direct Models via Local Velocity Propagation

1: Initialize parameters θ for v θ , ν for w ν

2: for each training step do

3: Sample pair ( x 0 , x 1 ) ∼ ( µ 0 , µ 1 )

4: Train velocity model v θ with CFM loss:

5: Sample t ∼ U [0 , 1]

6: Compute x t = (1 -t ) x 0 + tx 1 and

7: Minimize

with respect to θ

8: Update θ

9: Train residual field w ν with local propagation loss:

10: Sample t ′ ∼ U [ δt, 1 -δt ]

11: Compute x ′ t = x 0 + t ′ · sg [ w ν ( x 0 , t ′ )]

12: Minimize

with respect to ν

13: Update ν

14: end for

include unconditional generation on the CelebAHQ-256 dataset [11] and we also provide a comparison with class-conditional generation on ImageNet-256 [2] . For the results in Table 1 , we use the AdamW optimizer with a fixed learning rate of 5 × 10 -5 and no weight decay. Models are trained for 500K iterations, using a step size of δt = 10 -2 and batch size of 64 . Additionally, all models operate in the latent space provided by the sd-vae-ft-mse autoencoder [15].

4.2 Compared Methods

We compare our method to several prior approaches, following the same comparison setup as in [3]. For completeness, we briefly describe the training details of the compared methods based on the descriptions in [3].

We consider two categories of diffusion-based models: distillation methods, 1 which involve pretraining a diffusion model followed by distillation, and end-to-end methods, which train a one-step model from scratch in a single training run. As representatives of the first category, we include the standard diffusion model, following the setup of [14], and Flow Matching, which replaces the diffusion objective with an optimal transport loss as proposed in [9]. These serve as baselines for iterative multi-step denoising models. Several other methods build upon the flow matching objective, often utilizing a teacher model. Reflow [9] is a two-stage distillation technique that generates synthetic ( x 0 , x 1 ) pairs by fully evaluating a teacher model. Following [9], 50k synthetic samples are generated for CelebAHQ, with each requiring 128 forward passes. Unlike conventional distillation, the student model is trained across the full time interval t ∈ (0 , 1) . Progressive Distillation [16] adopts a binary time-distillation framework. Starting from a pretrained teacher, a sequence of student models is distilled, each trained with a step size that is double the previous one. The initial phase employs classifier-free guidance to enhance performance. Consistency Distillation [20] is a two-stage approach where the student model learns to predict consistent x 1 values from teacher-generated pairs ( x t , x t + δ ) . In contrast, Consistency Training [20] is an end-to-end method that trains a one-step model directly on empirical pairs ( x t , x t + δ ) , with time discretization bins increasing progressively during training. Shortcut models [3] propose a novel generative modeling framework that conditions on both the current noise level and desired step size, enabling efficient and flexible sampling under different inference budgets. Finally, Live Reflow, introduced in [3], is an end-to-end model trained

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simultaneously on flow-matching and Reflow-distilled targets. The model is conditioned separately on each type of target, and new distillation targets are generated at every training step via full denoising, making the method computationally expensive.

4.3 Evaluation

We follow the evaluation protocol from [3]. Models are evaluated by generating samples using 1 diffusion step for our method, and 128, 4, and 1 steps for the baselines. We report the FID-50k score, a standard metric in generative modeling. FID is computed using statistics from the full dataset, with no compression applied to the generated images. All images are resized to 299 × 299 using bilinear interpolation and clipped to the ( -1 , 1) range. During evaluation, we use the Exponential Moving Average (EMA) of the model parameters.

4.4 Results 168

Table 1 shows that Direct Models achieves strong generation quality using just a single sampling step. 169

Our method outperforms all single-stage training approaches in one-step generation and remains 170

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matching methods show a significant drop in performance when limited to 4 or 1 sampling step.

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4.5 Does Direct Models Induce a Semantically Coherent Latent Space?

To examine whether the latent space learned by Direct Models supports smooth semantic transitions, we explore linear interpolations in the input noise space. Specifically, we select pairs of initial Gaussian noise vectors ( x 0 0 , x 1 0 ) and interpolate between them using the variance-preserving formulation

where the coefficient n ∈ [0 , 1] . We then pass the interpolated noise samples through the model and observe the corresponding outputs.

Figure 2 presents representative samples from these interpolations. Despite the absence of any explicit constraint or regularizer enforcing smoothness in the learned mapping, the results reveal coherent and continuous transformations across the generated images. These transitions are not only visually smooth but also retain semantic consistency, suggesting that Direct Models constructs a meaningful latent structure.

5 Ablation

We investigate the effect of the discretization interval δt on image quality. As shown in Table 2, both values of δt , namely 10 -2 and 5 · 10 -3 , lead to very comparable FID scores (16.8 vs. 16.6).

6 Related Work

We briefly review existing approaches that enable single-step diffusion-based generation, which can be broadly categorized into distillation-based methods and single-phase training methods.

Distillation Methods In recent years, various techniques have been developed to distill generative models, particularly diffusion models, into more efficient one-step sampling frameworks. These methods typically follow a two-stage pipeline: first, a diffusion model is pretrained; second, a separate model is trained to approximate the behavior of the full diffusion process using fewer inference steps.

Methods such as knowledge distillation [12] and rectified flows [9] generate synthetic training pairs by fully simulating the reverse-time denoising ODE. Due to the high computational cost of full simulation, more efficient alternatives have been proposed that use bootstrapping strategies to partially initialize the ODE trajectory [4, 21]. Additionally, several works have explored alternatives to the standard L2 loss, including adversarial training objectives [17] and distribution-matching approaches [23, 22]. Progressive distillation techniques [16, 1, 13] further decompose the distillation process into multiple stages with increasing time step sizes, thereby reducing the need for long bootstrap paths.

In contrast to these methods, we propose an end-to-end training approach that directly learns a one-step generative model. This eliminates the need for separate pretraining and distillation phases, making our method simpler than both full simulation-based techniques and multi-stage progressive distillation.

Single-phase Training Methods Few methods have been proposed for single-phase training that enable single-step generation. Consistency Models [20], a pioneering approach in this area, represent a class of generative models that directly map partially noised data points to their final, fully denoised outputs in a single step. While these models have been effectively used in distillation purposes, they have also been explored the end-to-end training scenario. Shortcut models [3] propose a novel generative modeling framework that conditions on both the current noise level and desired step size, enabling efficient and flexible sampling under different inference budgets.

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Difference from consistency models [20] While we share the general concept of consistency with [20], Direct Models differs significantly in its formulation. Conceptually, Direct Models can be seen as the opposite approach: instead of mapping intermediate latents x t directly to the fully denoised image x 1 , our method maps initial Gaussian noise x 0 to all intermediate latent states x t , as shown in Figure 3.

Difference from shortcut models [3] Shortcut models are arguably the most similar approach to Direct Models. However, there are key differences: 1) Conceptually, Shortcut models learn direct mappings between all pairs of latent states, including both the initial and final ones. In contrast, Direct Models focuses on learning a direct mapping only between the initial Gaussian noise and all intermediate latent states. 2) More importantly, our approach is grounded on a more principled mathematical formulation. Specifically, we derive our method using a Taylor expansion of the flow, as shown in Equation (13), which links the flow at neighboring timesteps to the velocity field.

7 Limitations and Future Work

Our method presents some limitations. First, Direct Models requires training two separate networks, which limits efficiency. Second, the current formulation is restricted to single-step inference. A promising direction for future research is to extend our framework to enable training a single unified model while potentially allowing flexibility in the number of inference steps during sampling.

8 Conclusion

We introduced Direct Models, a new type of diffusion-based generative model that enables both single-step sampling and single-run training. By learning a time-indexed residual field to directly approximate the full generative flow, our method achieves fast and high-quality generation while significantly simplifying the training process. This makes Direct Models a practical and efficient alternative to existing diffusion-based techniques.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces Direct Models, a framework to perform single-step diffusion for image generation. The method is based on the flow matching concept, particularly the Conditional Flow Matching formulation [1]. The authors defined the flow phi(x,t) by x + tw(x,t) where w is parameterized by a neural network. The framework performed by first training the vector field v, by the formulation in [1], and then  w by matching (x + tw(x,t))’ with v. Finally, inference can then be carried out in 1 step using the learned w(x,t). Experiments with CelebAHQ-256 are provided, showing the method performs relatively well compared to other approaches.\n\n\n[1] Yaron Lipman, Ricky TQ Chen, Heli Ben-Hamu, Maximilian Nickel, and Matt Le. Flow matching for generative modeling\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Technically, the idea is sound. It tries to approximate the entire flow path in 1 step, using a  parameterization of the vector field.\n\n- The approach introduced is simple and easy to follow. The authors did a good job of explaining the core technical idea and results.\n\nWeakness:\n- The paper title “Single-step diffusion” is misleading. There is no diffusion process, the entire paper is constructed based on Flow matching.\n\n- The mention of “Taylor expansion” seems like an unnecessary jargon to me, it’s just a simple finite difference, there is no error quantification. Further more, equation (8) is confusing, since the authors are mixing continuous time and finite discrete time together.\n\n- The authors should be upfront with the fact that the framework operated in latent space using Stable diffusion encoder, instead of just passingly mention it in the experiments.\n\n- The comparison to Distillation method by saying “we propose an end-to-end training approach that directly learns one-step generative model” (line 205) is also misleading. The training actually depends on a well-trained vector field v(x,t), the authors, instead of using a trained v(x,t), decides to train v and w alternatively in the same training loop. I believe this will make the training less stable than finishing training v first, then use that signal to train w, in which case this is essentially a distillation process. In [3], the training is also done in 1 loop, alternatively, but the authors still mistakenly say that it’s not end-to-end compared to the paper under review. (Lines 202-206)\n\n- The evaluation is lacking, the authors only evaluate on 1 dataset of CelebAHQ. Since CelebA is a highly structured dataset (aligned human faces with good lighting conditions), the performance may not generalize to more diverse dataset like ImageNet. Also, the authors mentioned different distillation schemes, including [3], but only make comparisons to the 3 older methods published in 2022-2023, while the results claimed in [3] already surpassed them.\n\n- The submitted version looks very rushed in some sections. For example, the ablation study only contains 2 short sentences with no explanation of the results.\n\n- The authors failed to cite or make comparison against [2], which proposed 1-step flow matching, using a principled formulation.\n\n\n[2] Kornilov, Nikita, et al. \"Optimal flow matching: Learning straight trajectories in just one step.\" Advances in Neural Information Processing Systems 37 (2024): 104180-104204.\n[3] Yin, Tianwei, et al. \"Improved distribution matching distillation for fast image synthesis.\" Advances in neural information processing systems 37 (2024): 47455-47487.\n\nQUESTIONS:\n- The authors choose to parameterize phi in a specific way, how does this affect the path and quality of generated samples? We see in [1] that different parameterization can lead to highly different paths.\n\n- Would it be possible to have a single network approach?\n\n- There’s no analysis or discussion of stability over multiple timesteps\n\n- How would the model perform on different datasets? ie ImageNet\n\n- How well would it compare against 1-step flow matching?\n\n- What is the motivation behind the stop-gradient? It would be interesting to explore its effect.\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 1, "ORIGINALITY": 1, "DATE": "2025-07-01"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors introduce a generative modeling framework (\"Direct Models\") that enables single-step generation. To do this the authors learn both a velocity field and a residual field $w(x,t)$, where the latter object parameterizes the flow and can thus be used to do single-step generation. The velocity field is trained via a Conditional Flow Matching loss, while the residual field $w$ is trained via a \"Local Velocity Propagation\" loss that encourages (finite differences of) the residual field to be consistent with the velocity. Conceptually, Direct Models can be viewed as the \"opposite\" of Consistency models in that Direct Models map gaussian noise to all intermediate latents, while Consistency models map intermediate latents to the fully denoised datapoint. The result is a practical one-step generation method that is competitive with alternative approaches (at least as judged by the CelebAHQ-256-based empirical evaluation), including distillation-based methods and end-to-end methods like Consistency models.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n\n- The paper is clearly written and generally easy to follow\n- The method is conceptually simple, easy to understand, and entails a straightforward training procedure. As far as I know the method is novel.\n- The empirical performance, while limited to a single dataset, shows competitive performance with a mix of relevant baseline methods\n- The paper addresses a problem area, namely one-step generation, that is of interest to many in the community\n\nWeaknesses:\n\n- While generally clearly written, the submission is a bit sparse on some details (see below)\n- The empirical validation is limited to a single dataset. It would be particularly valuable to see more benchmarking in the class conditioned setting (i.e. beyond what's in the supplement).\n\nQUESTIONS:\nQuestions:\n- It's nice to see the mini-ablation in Table 2 but what happens at different $\\delta t$, for example $0.02$? Benchmarking only two choices limits what we can learn from this.\n- Have you tried non-uniform time sampling during training, especially for $t^\\prime$ in Eqn 16?\n- What do you expect would happen if you first trained the velocity field, fixed its parameters, and then learned the residual field via the local propagation loss? Or if you also computed $\\theta$ gradients for the \nlocal propagation loss? What trivial solutions, if any, do you need to guard against?\n\nComments:\n- Using parameters $\\nu$ instead of e.g. $\\phi$ is confusing, since $\\nu$ can be easily confused for the velocity.\n- Writing out all the elementary algebra between Eqn 8 and 12 and then repeating Eqn 12 as Eqn 13 is a waste of space. This space could be used much more profitably by clarifying other aspects of your method, see below. Similarly, the conditional generation results can/should be moved to the main paper.\n- Line 69: \"or sampling noise\". This is hopelessly vague; please clarify.\n- Line 134: \"Additionally, all models operate in the latent space provided by the sd-vae-ft-mse autoencoder.\" This is unnecessarily vague. Please be more specific.\n- Line 13 in the supplement: \"For the ImageNet case, we adopt classifier-free guidance (CFG) during training.” This is an entirely inadequate description. Please be much more specific, with equations.\n\nLIMITATIONS:\nYes, as mentioned by the authors, one limitation is that the current formulation is restricted to single-step inference.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces Direct Models, a framework for training single-step generative models. Direct Models map the initial noise $x_0$ to any intermediate time $t$. The model's evolution is governed by matching the derivative at the endpoint $x_t$. This is achieved by jointly training two networks: a standard conditional flow matching (CFM) model to estimate the velocity field, and the direct model that learns to map noise from t=0 to t=1 in a single inference step. The authors claim their method achieves state-of-the-art sample quality among single-step methods on CelebA-HQ.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n1. This paper is well-motivated in pursuing a high-quality, single-step generative model and addresses a significant bottleneck of inference speed in diffusion and flow-based models.\n2. The experimental results show improved FID scores compared to recent single-step models.\n3. The paper is generally well-written and the proposed method is described with good clarity for implementation.\n\n### Weaknesses \n\n1. The proposed Direct Models largely overlap with BOOT. Both models map noise to intermediate time steps, and the loss function matches the derivative (velocity or score) at the intermediate time steps. The `stop-gradient` is applied similarly. What is the benefits of Direct Models over BOOT?\n2. The \"single run\" claim does not seem valid in the present paper. Without a comprehensive comparison of distillation against training two models jointly, the claim that this method is \"more practical and efficient\" (line 25) is not supported.\n3. The manuscript presents inadequate ablation studies. The authors claim the formulation $x + w(x,t)$ leads to \"unstable training\" but provide no evidence. What if use large $\\delta t$? The impact of the `stop-gradient` in the propagation loss? Does the model fail to train without it?\n\nQUESTIONS:\n1. The Flow Matching model is jointly trained with Direct Models. There is no evidence that this Flow Matching model necessarily needs to be jointly trained with Direct Models. How large is the difference from using a pre-trained teacher model as $v_\\theta$?\n2. How does the training loss curve look?\n\nLIMITATIONS:\nAs discussed in the paper.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 5, "CLARITY": 3, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}