Title: One Step Diffusion via Flow Fitting
Venue: NeurIPS 2025
Accepted: no
Keywords: Efficient generative models

Single step diffusion
Abstract: Diffusion and flow-matching models have demonstrated impressive performance in generating diverse, high-fidelity images by learning transformations from noise to data. However, their reliance on multi-step sampling requires repeated neural network evaluations, leading to high computational cost. We propose FlowFit, a family of generative models that enables high-quality sample generation through both single-phase training and single-step inference. FlowFit learns to approximate the continuous flow trajectory between latent noise \(x_0\) and data \(x_1\) by fitting a basis of functions parameterized over time \(t \in [0, 1]\) during training. At inference time, sampling is performed by simply evaluating the flow only at the terminal time \(t = 1\), avoiding iterative denoising or numerical integration. Empirically, FlowFit outperforms prior diffusion-based single-phase training methods achieving superior sample quality.

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Abstract

Diffusion and flow-matching models have demonstrated impressive performance in generating diverse, high-fidelity images by learning transformations from noise to data. However, their reliance on multi-step sampling requires repeated neural network evaluations, leading to high computational cost. We propose FlowFit, a family of generative models that enables high-quality sample generation through both single-phase training and single-step inference. FlowFit learns to approximate the continuous flow trajectory between latent noise x 0 and data x 1 by fitting a basis of functions parameterized over time t ∈ [0 , 1] during training. At inference time, sampling is performed by simply evaluating the flow only at the terminal time t = 1 , avoiding iterative denoising or numerical integration. Empirically, FlowFit outperforms prior diffusion-based single-phase training methods achieving superior sample quality.

1 Introduction

In recent years, iterative denoising methods such as diffusion models [16, 5, 17] and flow matching 14 [7, 8] have achieved remarkable success across a wide range of generative modeling tasks, including 15 image synthesis, molecular generation, and audio modeling. These methods define a generative 16 process as the solution to a learned differential equation that progressively transforms simple noise 17 into complex data through a series of small, structured updates. Their strong empirical performance 18 stems from their ability to model complex distributions with stable training dynamics and flexible 19 architectures. 20

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However, a key limitation of these approaches lies in their sampling efficiency. Since generation is performed by solving a differential equation, typically through numerical integration, these methods often require hundreds of sequential function evaluations at inference time. This iterative sampling procedure can be computationally expensive, slow, and memory-intensive, limiting their practicality in real-time or resource-constrained settings.

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In this work, we aim to retain the modeling flexibility and training benefits of diffusion-based methods while enabling efficient single-step generation .

While recent work has explored accelerating inference in diffusion models through distillation, these approaches typically follow a two-stage training paradigm. In such methods, a pre-trained diffusion model is first learned through standard iterative training, and then a separate model is trained to mimic its behavior in fewer steps, usually by generating a large synthetic dataset of intermediate trajectories [10, 7] or propagating through a series of teacher and student networks [11, 14]. This introduces additional complexity, increases memory requirements, and may limit generalization due to reliance on a fixed teacher.

In contrast, we propose FlowFit, a unified, single-phase training approach that learns to generate 35 samples in one step from the outset. Our method directly parameterizes the entire flow using a 36

basis function expansion, enabling the model to learn global transport trajectories in a compact and 37

structured manner. Once trained, sampling from the model requires only evaluating the learned flow 38

at terminal time t = 1 , given a source point x 0 ∼ µ 0 (see examples in Figure 1). 39

A key insight motivating our approach is that a smooth transformation, such as a flow trajectory, 40

can be directly fitted using the initial value and all its time derivatives. By fitting the trajectory 41

using a set of basis functions anchored at the initial point, we capture the flow's global behavior and 42

bypass the need for iterative integration. This allows us to retain the expressive modeling capacity of 43

continuous-time methods while achieving orders-of-magnitude faster sampling. 44

We train the model to ensure that the trajectory is consistent with a learned velocity field through a 45

combination of Conditional Flow Matching and a trajectory-velocity consistency loss. Additionally, 46

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we introduce a progressive training strategy that improves stability and alignment between the flow

and velocity in early training stages. 48

Our main contributions can be summarized as follows 49

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We propose a novel formulation for flow modeling via basis function fitting. FlowFit, a new generative modeling framework that directly parameterizes continuous-time flows using a residual expansion over fixed basis functions. This allows the model to represent entire flow trajectories with a compact, structured parameterization. To the best of our knowledge, FlowFit is the first to propose such a formulation.

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We demonstrate that FlowFit achieves sample quality better or on par with existing single step diffusion-based approaches .

2 Related Work 57

We review prior research efforts aimed at accelerating diffusion-based generative models through 58

single-step sampling. Existing approaches generally fall into two categories: those based on multi59

stage distillation and those relying on direct, single-phase training. 60

2.1 Two-Phase Training Approaches 61

A common strategy for improving inference efficiency involves distilling multi-step diffusion models 62

into simpler one-step samplers. These techniques typically follow a two-phase process: a full 63

diffusion model is trained first, and then a lightweight student model is optimized to mimic its 64 behavior over fewer denoising steps. 65

Several works adopt this paradigm by simulating the full denoising trajectory to generate supervision 66 pairs, as seen in knowledge distillation [10] and rectified flows [8]. While effective, these methods 67 are computationally intensive due to the need for full reverse-time ODE evaluations. To mitigate this, 68 more recent efforts introduce bootstrapping mechanisms that shorten the ODE simulation path [4, 19]. 69 Additionally, researchers have explored a variety of loss functions beyond the traditional L2 objective, 70 including adversarial criteria [15] and distributional matching techniques [21, 20]. 71

Progressive distillation [14, 1, 11] offers a multi-stage solution, wherein a sequence of student models 72 is trained with progressively larger time steps. This hierarchical approach reduces the dependency on 73 costly long-path bootstrap samples. 74

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Our proposed method diverges from these frameworks by eliminating the need for both pretraining and distillation. Instead, it adopts a unified, end-to-end training scheme that learns a single-step generator directly, simplifying both the implementation and training pipeline.

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2.2 Single-Phase Training Approaches

Only a limited number of methods have been developed for one-step generation via single-stage 79 training. Among the first of its kind, Consistency Models [18] learn to map noisy inputs directly to 80 their clean counterparts in a single forward pass. Although originally designed for distillation, they 81 have also been extended to an end-to-end training setup. 82

Shortcut models [3] introduce a flexible generative approach that allows conditioning on both the 83 input noise level and the desired step size, enabling inference under various computational constraints. 84

While FlowFit shares the general concept of consistency with [18] and [3], it is significantly different. 85 To the best of our knowledge, FlowFit is the first method to directly aim for a single-step diffusion 86 model using a basis of functions. 87

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3 Preliminary: Diffusion and Flow Matching

Recent advances in generative modeling have led to the development of methods such as diffusion models [16, 5, 17] and flow-matching approaches [7, 8], which learn a continuous-time transformation from a simple noise distribution to a complex data distribution. These models typically define the generative process through an ordinary differential equation (ODE), where the time-dependent dynamics are learned to guide samples from noise toward data.

In this work, we adopt the flow-matching formulation based on the optimal transport objective introduced by [8], as it offers a simple and effective framework for learning such dynamics. While diffusion models and flow-matching approaches are often studied separately, recent perspectives, such as that of [6], highlight that flow matching can be interpreted as a deterministic special case of diffusion modeling. Accordingly, we treat the two paradigms as closely related and use the terminology interchangeably where appropriate.

Flow Matching provides a supervised learning framework for modeling deterministic, continuoustime flows that transport a base distribution µ 0 (e.g., standard Gaussian) into a target distribution µ 1 (e.g., data distribution). Drawing from optimal transport and neural ODEs, it directly learns a velocity field that defines a transport trajectory between paired samples.

Let x 0 ∼ µ 0 be a sample from the source distribution and x 1 ∼ µ 1 its corresponding target. The model learns a time-dependent velocity field v θ ( x, t ) such that solving the associated ODE transforms µ 0 into µ 1 . Formally, the flow is described by

where u t : [0 , 1] × R d → R d is a neural network parameterizing the velocity field, and ψ t ( x ) is the 107 flow map at time t . 108

A common training strategy is to supervise the model using velocity information along linear paths 109 between x 0 and x 1 , evaluated at intermediate points (1 -t ) x 0 + tx 1 . The corresponding ground-truth 110 velocity at such a point is simply x 1 -x 0 . 111

The model is then trained to match this known velocity at intermediate points. The Conditional Flow 112 Matching (CFM) objective function is defined as 113

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This loss guides the model to predict the instantaneous velocity field that aligns with the linear flow between samples. Notably, this avoids the need for computing density functions or score gradients, distinguishing it from traditional diffusion models.

Once training is complete, sample generation begins by drawing an initial point x 0 ∼ µ 0 , typically from a standard Gaussian distribution. This point is then transformed toward the data distribution by solving the learned ODE defined by the velocity field v θ ( x, t ) . In practice, this continuous-time flow is discretized and approximated using numerical integration methods such as Euler's method, where the sample is updated iteratively over a sequence of small time steps from t = 0 to t = 1 .

4 FlowFit: Direct Flow Parameterization via Basis Function Fitting

In this section, we introduce FlowFit, a novel approach for modeling continuous-time flows via basis function fitting. Specifically, we aim to directly parameterize the flow ψ t ( x ) using a basis of functions that are conditioned on both the initial point x 0 and the time parameter t . Thus, the goal is to model the mapping ( x 0 , t ) ↦→ ψ t ( x ) = x t , where ψ t ( x ) is the flow at time t , and x t represents the transformed point at time t .

To this end, we approximate the true flow ψ t ( x ) with a learnable function ψ θ ( x 0 , t ) 1 , parameterized via neural networks and basis functions. For simplicity, we use the notation x t interchangeably with both ψ t ( x ) and ψ θ ( x 0 , t ) , with the dependence on x 0 and t understood implicitly. This allows us to define the transformation in terms of a set of basis functions, which we leverage to approximate the flow dynamics. Importantly, this representation enables efficient single-step generation by evaluating the learned trajectory at t = 1 , and requires only the initial sample x 0 ∼ µ 0 at inference time.

4.1 Trajectory Parameterization

We approximate the continuous flow trajectory using the time-dependent formulation

{ γ k ( t ) } K k =1 are fixed scalar basis functions (e.g., polynomial or Fourier),

f θ,k : R d → R d are neural networks that produce the coefficients,

θ denotes all learnable parameters.

A first question is whether one can approximate arbitrarily well the trajectory ψ ( x, t ) with the above basis expansion. This is a rather straightforward result that we report in the Appendix for completeness.

4.2 FlowFit Training

We jointly train two models: ψ θ , which parameterizes the flow trajectory, and v θ ′ , which models the time-dependent velocity field. To ensure that the learned trajectory ψ θ ( x 0 , t ) evolves in alignment

where

with the correct transport dynamics, we supervise it by matching its time derivative to a known target 146 velocity field. Taking the derivative of the basis function parameterization gives 147

Simultaneously, the velocity model v θ ′ ( x, t ) is trained using the standard Conditional Flow Matching 148 (CFM) objective. In this setup, a source point x 0 is randomly sampled from the base distribution 149 µ 0 and a target point x 1 is independently sampled from the data distribution µ 1 . The model is then 150 trained to match the ground-truth velocity ˜ v ( x 0 , x 1 , t ) = x 1 -x 0 at intermediate points along the 151 linear interpolation between x 0 and x 1 . The loss is given by 152

To align the basis-induced flow with the learned velocity field, we require that the velocity induced 153 by the basis-function trajectory matches the prediction of the velocity model at the corresponding 154 location along the flow 155

We formalize this requirement with a loss that enforces matching the flow derivative to the velocity 156

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where sg [ · ] denotes the stop-gradient. This loss encourages the parameterized trajectory to follow a velocity field that is internally consistent with the learned dynamics, improving the alignment between the path and the underlying transport vector field.

Despite the fact that ψ θ ( x 0 , t ) may initially provide limited information early in training, we observe that the propagation loss remains robust and effective. This eliminates the need for manually scheduling t , thereby simplifying the training process and enhancing both stability and usability, all without sacrificing performance. The full training algorithm and the corresponding sampling procedure are outlined in Algorithm 1 and 2.

4.3 Single-Step Generation

At inference time, the model generates samples from the target distribution µ 1 by drawing x 0 ∼ µ 0 and evaluating the fitted trajectory at terminal time:

This enables fast and deterministic generation without iterative integration, in contrast to diffusion or traditional flow-based models.

5 Experiments

5.1 Experimental Setup

Weevaluate our method alongside a range of established baselines under consistent training conditions. 172 To ensure fairness, all models are trained from scratch using an identical implementation and share the 173 same backbone architecture, the DiT-B diffusion transformer [12]. Our evaluation includes two tasks: 174 unconditional image generation on the CelebAHQ-256 dataset [9]. In our supplementary, we also 175 provide a comparison with class-conditional generation on ImageNet-256 [2] . For the experiments 176 reported in Table 1, we use the AdamW optimizer with a constant learning rate of 4 × 10 -5 , no 177 weight decay, and train each model for 500K iterations. We use a Polynomial basis with order 8 . All 178 models are trained and sampled in the latent space provided by the sd-vae-ft-mse autoencoder [13]. 179 Additional experimental details and our codebase are available in the supplementary material. 180

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5.2 Baseline Approaches

We benchmark our approach against a diverse set of generative models, closely following the evaluation protocol introduced in [3]. The results for the competing methods, shown in Table 1, are taken from [3]. For clarity, we briefly summarize the training procedures of the baseline models as described in that work. The baselines fall into two main categories: two-phase training models , which distill fast samplers from pretrained diffusion models, and end-to-end models , which are trained from scratch to perform generation in a single step.

In the distillation category, we include the standard diffusion model, following the setup from [12], and Flow Matching [8], which replaces the diffusion objective with a transport-based loss. Reflow [8] is a representative distillation method that generates 50k synthetic ( x 0 , x 1 ) pairs on CelebAHQ using a teacher model requiring 128 forward passes per sample. The resulting student is then trained over the full time interval t ∈ (0 , 1) . Progressive Distillation [14] iteratively distills a sequence of student models, each trained with a step size double that of its predecessor, starting from a classifier-free guided teacher. Consistency Distillation [18] trains the student model to predict final samples from intermediate pairs generated by the teacher.

In contrast, end-to-end methods eliminate the need for a teacher model. Consistency Training [18] trains a single-step model directly by enforcing consistency between empirical sample pairs ( x t , x t + δ ) , with progressively increasing time intervals during training. Shortcut models [3] introduce step-size conditioning, allowing for flexible generation across varying inference budgets. Finally, Live Reflow [3] jointly trains on both flow-matching and Reflow-distilled targets, regenerating new targets at each training step via full denoising from a flow-matching teacher. While this yields strong performance, it incurs significant computational cost.

5.3 Evaluation Protocol

We follow the evaluation framework established in [3]. Each model generates 50k samples for computing the FID-50k score. Our method is evaluated using a single-step sampler, while the baseline models are assessed under 128-step, 4-step, and 1-step variants. FID-50k is calculated using statistics from the full dataset, with no compression applied to the generated samples. All images are resized to 299 × 299 via bilinear interpolation and normalized to the [ -1 , 1] range. During inference, we apply the Exponential Moving Average (EMA) of the model parameters to improve stability and performance.

5.4 Comparison

Table 1 highlights that FlowFit delivers high-quality generations in the single sampling step. Notably, it surpasses all other single-phase training methods in one-step generation performance and performs on par with progressive distillation techniques that require multiple training stages. In contrast

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to these multi-stage approaches, FlowFit achieves its results within a single training phase. As anticipated, conventional diffusion and flow-matching models experience a notable decline in sample quality when constrained to just 4 or 1 inference steps. We include further qualitative examples in the supplementary material.

5.5 Semantic Structure in the Latent Space of FlowFit

To assess whether FlowFit gives rise to a semantically meaningful and smooth latent space, we perform an interpolation experiment in the input noise domain. We begin by selecting pairs of Gaussian noise vectors x 0 0 and x 1 0 , and interpolate between them using a variance-preserving scheme x n 0 = nx 1 0 + √ 1 -n 2 x 0 0 with n ∈ [0 , 1] . Each interpolated point x n 0 is then processed through the trained model to generate the corresponding output. Figure 2 shows representative results from this interpolation. Even though no explicit smoothness constraints or regularization terms are imposed during training, the outputs exhibit continuous and visually coherent changes. The interpolated generations preserve high-level semantics while gradually morphing between endpoints, indicating that FlowFit captures an underlying latent structure that supports semantically consistent transitions.

6 Ablations

6.1 Effect of Basis Order

We investigate how the order of the polynomial basis affects the resulting image quality. In Table 2, 231 we present results for two polynomial basis orders under the same training conditions: order 2 with 232

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basis functions { t k } 2 k =1 and order 8 with basis functions { t k } 8 k =1 . Our findings show that using a higher-order basis leads to improved image quality.

6.2 Effect of the Basis Type

We evaluate the influence of the basis function type on generation quality while keeping the expansion order fixed. Specifically, we use { t k } 8 k =1 for the polynomial basis and { cos(2 kπt ) } 4 k =1 ∪ { sin(2 kπt ) } 4 k =1 for the trigonometric basis. As reported in Table 3, the polynomial basis yields a better FID score of 14.1 compared to the trigonometric basis (16.3).

Limitations and Future Work

While FlowFit demonstrates strong performance, it also has certain limitations. One notable drawback is the requirement to train two separate networks, which may lead to increased computational overhead. Moreover, the current design is restricted to single-step inference. A promising direction for future research is to generalize the framework to support a unified model architecture that enables flexible sampling with a variable number of inference steps.

Due to computational constraints, we explore the method up to order 8 in this work. It would be interesting to investigate higher-order expansions and assess their impact. Another potential direction is to explore alternative basis functions in the formulation.

7 Conclusion

We introduced FlowFit, a novel diffusion-based generative model that enables both single-step sampling. The core idea behind our approach is a new formulation for flow modeling based on basis function fitting. FlowFit delivers fast, high-quality generation while substantially simplifying the training process, making it a practical and efficient diffusion-based method.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes to parametrizes flow trajectories by linear combination of basis functions where basis functions take analytical form and coefficients of the basis functions are learned by neural networks. The parameterized flow map is decoupled in that the basis function depends on t and the neural network depends on the initial condition $x_0$. The time derivative can then be done analytically without automatic differentiation. A joint training strategy is proposed, where a normal flow matching network is trained and a second, FlowFit network is trained together which distill the flow matching network in an online fashion.\n\nSTRENGTHS AND WEAKNESSES:\nStrength:\n- The idea of decoupling time and space where one can learn space via neural network is neat, and one does not need automatic differentiation to calculate flow map derivative. \n- The proposed method is easy to understand.\n- One-step results on CelebAHQ outperforms prior end-to-end methods. \n\nWeaknesses:\n- While I recognize that the novelty lies in decomposing the flow map into independent space and time components, the proposed distillation method is the same as Physics Informed Distillation [1], which leverages principles from Physics Informed Neural Networks. However, this paper fails to discuss, compare, or even cite this prior work. A proper discussion and comparison is needed.\n- The empirical investigation is limited, as the paper only compares results on CelebAHQ. How about CIFAR10 and ImageNet? How does this method compare with recent prior methods such as [2].\n- The sinusoidal embedding used in normal flow matching networks uses cosine and sine basis for their time embedding layers, but they additionally embed these basis functions into neural networks to obtain more complex functions of $x$ and $t$. It does seem that multiplying the basis funtions direct with neural networks severely limit their representational capacity. Or at least this seems to require significantly more complex neural networks to fit complex joint (x,t) functions. There may not even exist an arbtrarily complex neural network to represent the joint (x,t) function fully. The authors do not seem to address this theoretical limitations in their discussion.\n\n\n[1] Tee, Joshua Tian Jin, Kang Zhang, Hee Suk Yoon, Dhananjaya Nagaraja Gowda, Chanwoo Kim, and Chang D. Yoo. \"Physics informed distillation for diffusion models.\" arXiv preprint arXiv:2411.08378 (2024).\n\n[2] Zhou, Linqi, Stefano Ermon, and Jiaming Song. \"Inductive moment matching.\" arXiv preprint arXiv:2503.07565 (2025).\n\nQUESTIONS:\nI'd like the authors to address my questions above. A proper discussion on prior methods and more empirical evaluations are needed. I believe the paper, although exhibiting novelty in its idea, is not ready for publication yet.\n\nLIMITATIONS:\nSome but not all technical limitations are addressed. No societal impact discussion is needed.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-24"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposed FlowFit for one-step or few-step generation for flow-based generative models. Specifically, the authors proposed directly learning the time-dependent trajectory, parameterized by a set of basis functions. By enforcing the consistency loss between the derivative of the flow and the vector field, the proposed FlowFit can achieve easy one-step generation. Experiments on the CelebAHQ dataset demonstrated better one-step generation quality.\n\nSTRENGTHS AND WEAKNESSES:\n## Strenghth\n- To the best of my knowledge, the proposed approach of utilizing a consistency-based loss is novel in comparison to existing consistency models.\n- On CelebAHQ, the proposed approach outperformed existing methods in one-step generation.\n\n## Weakness\n- Although the idea is new, this draft is clearly incomplete and lacks many details in theoretical validity and experimental setups.\n- The second condition in Equation 3 (the initial condition) prevents the model from collapsing, as an arbitrary constant added to the learned model will also satisfy the derivative constraint. This was never explained in the paper.\n- The experiments' scopes are limited. For example, the current evaluation focused on end-to-end training, although it is clear that the proposed approach can also do distillation (two-phase) of a pre-trained flow-based model, as the consistency loss is essentially independent.\n- Newer consistency baselines are not compared, e.g., iCT/iCD [1], sCD/sCT [2], which exhibit significantly better performance than the Reflow and other distillation baselines in this paper.\n- There are noticeable formatting mistakes, e.g., the \"time window $\\alpha_t$\" that was never used in Algorithm 1.\n\n[1] Song, Yang, and Prafulla Dhariwal. \"Improved techniques for training consistency models.\" arXiv preprint arXiv:2310.14189 (2023).\n\n[2] Lu, Cheng, and Yang Song. \"Simplifying, stabilizing and scaling continuous-time consistency models.\" arXiv preprint arXiv:2410.11081 (2024).\n\nQUESTIONS:\n- How to enforce the boundary condition in Equation 3 (Weakness 2)?\n- It is unclear why the authors chose to use a basis set instead of directly modeling the trajectory as one single network $\\psi_\\theta(x_0,t)$.\n- In Equation 7, it is unclear why the stop-gradient operator is used. Is it necessary for the consistency loss, or is it purely for computational concerns?\n- As the proposed approach can be easily adapted for distillation, it would be more beneficial to compare such results (Weakness 3).\n- sCM (Weakness 4) provided a robust baseline. Additional results with sCM would better demonstrate the effectiveness of the proposed approach.\n- The baseline results are identical to those in the Shortcut model paper. If the authors used these results, they should properly credit the original paper. Similarly, Section 5.5 is almost identical to that in the Shortcut model.\n\nLIMITATIONS:\nThe authors have discussed the potential limitations of this work.", "TITLE": "Official Review", "RECOMMENDATION": 3, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-06-28"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe following work proposes a single stage training algorithm for single-step sampling from probability flow ODEs (including, but not limited to flow matching, consistency models). The algorithm directly fits to the flow map solution at time t, bypassing the need to integrate over time during the sampling phase. This is achieved by representing the time-dependent ODE with either a Fourier (sinusoidal) or polyomial set of time-varying basis functions. The training algorithm alternates between fitting a standard vector field model $v_t$, then matching the derivative of the basis function model to the vector field with a consistency loss.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths:\n- Formulation and writing were clear and easy to understand\n- Method appears effective and principled\nWeaknesses:\n- I think prior work [1] uses a closely related formulation by also modeling the sampling trajectories in the Fourier domain -- allowing them to also achieve 1-step sampling.\n- Whether one would really consider this a single-stage training algorithm is perhaps a bit nuanced. Based on my understanding of the algorithm, we can maybe interpret this as distilling the vector field model into the FlowFit model while vector field model is still training. It's not clear that this is more efficient than just allowing the standard vector field model to train to completion on its own first, and then freezing it and distilling it to the FlowFit model. Furthermore, I believe progressive distillation can also be similarly formulated to train multiple stages simultaneously within the same training loop.\n- I feel like the comparison between polynomial and trigonometric basis functions shouldn't be written this conclusively, as it does not preclude the existence of an unused configuration of trigonometric basis functions that might yet yield better results.\n\n[1] https://proceedings.mlr.press/v202/zheng23d.html\n\nQUESTIONS:\n- Include relevant discussion wrt. prior works such as [1], highlighting differences and similarities\n- Respond to concern regarding single stage training claims.\n\nLIMITATIONS:\nLimitations were included, but societal impact was not. It might be a good idea to include a standard blurb regarding the negative impact of generative models.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 3, "CLARITY": 4, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-01"}