PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator
Authors: Hanshu Yan
Xingchao Liu
Jiachun Pan
Jun Hao Liew
qiang liu
Jiashi Feng
Venue: NeurIPS 2024 poster (2024)
Keywords: Flow Model
Diffusion Model
Generative Model
Image Generation
Primary area: diffusion_based_models

Abstract: We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the PeRFlow models inherit knowledge from the pretrained diffusion models. Thus, the training converges fast and the obtained models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models.

PeRFlow: Piecewise Rectified Flow as Universal Plug-and-Play Accelerator
Hanshu Yan", Xingchao Liu", Jiachun Pan", Jun Hao Liew", Qiang Liu", Jiashi Feng" "ByteDance, *Univeristy of Texas at Austin, *National University of Singapore
han outlook..om
Abstract
We present Piecewise Rectified Flow (PeRFlow), flow-based method for acceler- ating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piccewise linear flows. PeRFlow achieves superior performance in few-step generation. Moreover, through dedicated parameterizations, the PeRFlow models inherit knowledge from the pretrained diffusion models. Thus, the training converges fast and the obtained models show advantageous transfer ability, serving as universal plug-and and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. Codes for training and inference have been publicly released.
1 Introduction
Diffusion models have exhibited impressive generation performances across different modalities, such as image [34. 9, 39, 2]. video [10, 55, 42. 15, 48], and audio [11]. Diffusion models generate samples by reversing pre-defined complicated diffusion processes, thus requiring many inference steps to synthesize high-quality results. Such expensive computational cost hinders their deployment [14, 40, 31] real-world applications.
Diffusion models can be efficiently sampled by solving the corresponding probability flow ordinary differential equations (PF-ODEs) [39, 38]. Researchers have designed many advanced samplers, such as DDIM [38], DPM-solver [24], and DEIS [53], to accelerate generation, inspired by the semi-linear structure and adaptive solvers in ODEs. However, these samplers still require tens of inference steps to generate satisfying results. Researchers have also explored distilling pretrained diffusion models into few-step generative models [35, 28, 5, 50, 30. 31, which have succeeded in synthesizing images within 8 inference steps. Progressive Distillation [35] separates the whole sampling process into multiple segments and learns the mapping from starting points to endpoints for each segment. Distribution Matching Distillation [50] and SwiftBrush [30] use the score distillation loss to align the distributions of teacher and one-step student generators. UFOGen [47], SDXL-Turbo [36] and SDXL-Lightning [16] resort to adversarial training for learning few-step/one-ster image generators. They initialize the students from pretrained diffusion models and use adversarial and/or MSE losses to align the student model's generation with the pretrained ones. These methods suffer from the difficult tuning the adversarial training procedure and the mode collapse issue. Latent Consistency Model (LCM) [26, 27] adopts consistency distillation [40] to train generator that directly maps noises to the terminal images. LCM only utilizes supervised distillation where the training procedure will be more stable and easier in comparison to adversarial training. However, the generated images have fewer details compared with SDXL--Lihhing.
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38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Unlike the existing methods above, which mainly learn the mappings from noises to images, we aim to simplify the flow trajectories and preserve the continuous flow trajectories of the original pretrained diffusion models. Specifically, we attempt to straighten the trajectories of the original PF-ODEs via a piecewise reflow operation. Previously, InstaFlow [21] leverages the rectified flow framework[20, 19] to learn the transformation from initial random noise to images. It bridges the two distributions with linear interpolation and trains the model by matching the interpolation. With the reflow operation, it may be able to learn straight-line flows for one-step generation via pure supervised learning. InstaFlow provides simple pipeline for accelerating pretrained diffusion models, however, it suffers from poor sampling quality which can be attributed to synthetic data generation. The reflow operation requires generating data from the pretrained diffusion models with ODE solvers (e.g.. DDIM or DPM-Solver [24, 25]) to construct training dataset. Synthesizing training data brings two problems: (1) constructing and storing the dataset requires excessive time and space, which limits its training efficieney; (2) synthetic data has noticeable gap with real training data in quality due the numerical error of solving ODEs. Thus, the performance of the learned straighter flow is bounded.
To address the problems, propose piecewise rectified flow (PeRFlow), which divides the flow trajectories into several time windows and conducts reflow in each window. By solving the ODEs in the shortened time interval, PeRFlow avoids simulating the entire ODE trajectory for preparing the training data. This significantly reduces the target synthesis time, enabling the simulation to be performed in real time along with the training procedure. Besides, PeRFlow samples the starting noises by adding random noises to clean images according to the marginal distributions, and solves the endpoints of shorter time interval, which has lower numerical error than integrating the entire trajectories. Through such a divide-and ande--uud strategy, PeRFlow can straighten the sampling trajectories with large-scale real training data. Besides the training framework, we also design dedicated parameterization method for PeRFlow to inherit sufficient knowledge from the pretrained diffusion models. Diffusion models are usually trained with e-prediction, but flow-based generative models generate data by following the velocity field. We derive the correspondence between e- prediction and the velocity field of flow, thus narrowing the gap between the pretrained diffusion models and the student PeRFlow model. Consequently, PeRFlow acceleration converges fast and the resultant model can synthesize highly-detailed images within very few steps. PeRFlow does not require unstable adversarial training or a complete modification of the training paradigm. It is a lightweight acceleration framework and can be easily applied to training uncondiiional/condiionn generative models of different data modalities.
We conducted extensive experiments verify the effectiveness of PeRFlow accelerating pretrained diffusion models, including Stable Diffusion (SD) 1.5, SD 2.1, SDXL [32], and AnimateDiff [6]. ReRFlow-accelerate models can generate high-quality results within four steps. Moreover, we find that the variation of the weights, AW = 0 ø, between the trained student model 0 and the pretrained diffusion model ø, can serve as universal accelerators of almost all workflows that are only trained on the pretrained diffusion models. These workflows include customized SD models, ControlNets, and multiview 3D generation. We compared PeRFlow with state-of-the -o-t---rr-ttttttt acceleration methods. PeRFlow shows advantages in terms of FID values, visual quality, and generation diversity.
In summary, PeRFlow has the following favorable features: 1) it is simple and flexible for acceler- ating various diffusion pipelines with fast convergence: 2) The accelerated generators support fast generation: 3) The obtained AW shows superior plug-and-play compatibility with the workflows of the pretrained models.
2 Methodology
2.1 Rectified Flow and Reflow
Flow-based generative models aim learn a velocity field vo(2,,)) f) that transports random noise #1 ~ Ti sampled from a noise distribution into certain data distribution žy ~ Tp. Then, one can generate samples by solving (1) from t to 0:
dz, uo(z,, t)dt, 21 πi.
Recently, simulation-free learning of flow-based models has become prevalent [20, 19, 18, 1]. A representative method is Rectified flow (20, 19, 18), which adopts linear interpolation between the noise distribution 2 and the data distribution Zp. It trains neural network Vs to approximate the
2

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Original Probability Curved Trajectorio:; Slapy-Step
Plecewise Reflowed Model
Piecewise Lineur Trajecturies; Few Step
M T
Reflow
0.5
0.5
Reflow
11
11
Figure 1: Our few-step generator PeRFlow trained by a divide-and-conquer strategy. We divide the ODE trajectories into several intervals and perform reflow in each time window to straighten the sampling trajectories.
velocity field via the conditional flow matching loss. The corresponding optimization procedure is termed reflow [20, 19],
V [|[=1 - =0) no (z) (112
min E Roo
with 22 = (1 =0 + 1z1-
(2)
InstaFlow [21] proposed to accelerate pretrained Given a pretrained diffusion model fe. one can generate new data by solving the corresponding probability flow ODE. We denote (= f, s) as the ODE solver, such the DPM-Solver [23]. For simplicity, our notation drops the parameters in the ODE solvers. By simulating with zu ((21. 1), where 21 is sampled from the random Gaussian distribution Ti, it synthesizes a dataset of (text, ncise, image) triplets for reflow. Since it usually takes tens of inference steps to generate high-quality data with ((z), 1, 0), InstaFlow is expensive to scale up. Moreover, since InstaFlow trained with generated images, it lacks the supervision of real data and thus compromises the resulting generation quality. the following subsections, we target solving these problems.
cesttusioon-aaseee text-to-image models via reflow.
2.2 Piecewise Rectified Flow
We present Piecewise Rectified Flow (PeRFlow), aiming at training a piecewise linear flow to approximate the sampling process of pretrained diffusion model. PeRFlow sticks the idea of trajectory straightening. further allows using high-quality real training data and one- one-the-fi the-fly optimization. PeRFlow easier to scale up and succeeds in accelerating large-scale diffusion models, including the Stable Diffusion family.
A pretrained diffusion model fo corresponds to probability flow ODE defined by noise schedule (t). In the Stable Diffusion family, the forward diffusion process follows z; /I -1- =2(() (1)e, where Zy and are sampled from the data distribution and random Gaussian respectively. The sampling trajectories are usually complicated curves. Even for an advanced ODE solver (< s). it still requires many steps to generate an artifact-fre free image. We accelerate the pretrained model by applying divide-and-conquee strategy, that is, we divide the ODE trajectories into multiple time windows and straighten the trajectories in each time window via the reflow operation.
We create K time windows {[t,, 4x- 1)]) where 1 tx For each time window [ta, 1)-1), the starting distribution Ta will be the marginal distribution of the diffusion process at time tę. It can be derived from 2t, = v11 2² (tx)2z + attg)e. The target end distribution πę-1 constructed by ((212 . the 1x-1). We train the PeRFlow model, denoted by 0, to fit the linear interpolation between Zz, and 2t,-1 for all 1e E @1,1.... [1...., K.....K]. K].
> fx-1 >
Z4--1 Z8z
min
E
vo vo(2), 2)
dt
21
t tk
t 8-th-1 th-
tx -
with Z4e-
$ Zie 4, 4-1)
and 2t tu 1x-1
2tc
1--1 Zue-"
tv
Parameterization The pretrained diffusion models are usually trained by two parameterization tricks, namely e-prediction and velocity To inherit knowledge from the pretrained network.

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we parameterize the PeRFlow model as the same type of diffusion and initialize network & from the pretrained diffusion model 6. For the velocity-prediction we can train the PeRFlow model by matthing in (3). To accommodate e-prediction, we can represent the denoised state -
with the starting state 2t, and
-
A1 + C
(4)
where 2 > and Th are defined by the user. We propose to train a neural network cg t) to estimate the noise in (4) based on & for all t E [t&, tx1)):
K
2
2tc
min
E 3
cal22 co(zc;
dt
wikk
(5)
- 1k-1
Lx
with -/--1 ① ((1t, (te, les 1
and
2t to tk
21. +
Zte Zte-1"
t tk-1
The optimum of (3) and (5) are,
21ke Zle 22] [
da Ren
0" Zt, 1)
and c(2,,))
2t
tk- t
7]
Using calculus and the fact 2t
1-12-1
Zta + bx-1
F 1 1- we get,
1/ 14-1--1
(2,,t) (1 >x)=z me (z ()
(6)
t- tx-11 + dutR Aut
The sampling process involves first computing c0 t) from 2,, then estimating the velocity v(z)) via (6) for solving the ODE (1). In this paper, consider two choices for À and ny:
Purameterizatiion [A]: According to the definition of the diffusion process, we have Ztc
72t, + /1 78e with 7 = o 1 We can represent 2t, with 21, and
yield,
o. o
o of
A
TR
o
Parameterization [B]: We can also follow the DDIM solver [38], i.e.,
Otz-l
atc-
ass
Zta-1
V
+ to
V
Eo ( tx).
Ctty
Ore-
Oity
where 0g = 1 oh. We can correspondingly set,
y O
(k
d
Th
atte-1
(8)
Var
/
Org
This parameterization initializes the student flow from the update rule of DDIM, which is equivalent to the Fuler discretization of the probability flow ODE. We empirically observe that gives faster training convergence.
Scaling Up with Real Training Data PeRFlow divides the time range [1, 0 into multiple windows. For each window, the starting point zt,, is obtained by adding random noise to real training data 2o. and it only requires several inference steps to solve the ending point -1,- The computational cost is significantly reduced for each training iteration compared to InstaFlow, allowing to train PeRFlow on large-scale training datasets with fast online simulation the ODE trajectory. Besides, solving endpoints of shorter time window [žt, =t,_,) has lower numerical errors in comparison to the entire time range. High-quality supervision yields significant improvement in the generation results.
Classifier-Free Guidance in Training Classifier-fres guidance (CFG) [7] is common technique to improve the generation quality of text-to-image models. During training, we solve the endpoints Zt, for each time window [/,, 4a-1) in an online manner via an ODE solver o LR. 44-1, 1, c, w).
where w 2 denotes the CFG scale, denotes the text prompt. CFG is turned off when PeRFlow supports two modes: CFG-sync and CFG-fixed:

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Algorithm 1: Piecewise Rectified Flow
Input:
Training dataset D, <- or u-prediction teacher model fo. Noise schedule (1), ODE solver 8,, fa), Number of windows K, student model co or to.
Create K time windows {(42-1 (+)== with ix = 1 and l0 = 0
Initialize 0 o;
repeat
Sample 20 ~ D:
Sample & from {1, K) uniformly, then randomly sample time t E (tx-1, tx] Sample random noise e I0,
Get 21, - (14))22 + (1x)e;
Solve the endpoint of the time window z4.1 (2te 41)
10
Get 2, = Zt, 42-14-1
Fty -tp-1 (1 1x):
11
if e-prediction then
12
Compute loss
= co( t)
Sth -ARKKe
9/6
else 13
Compute loss = [uo(ze, 1x--
x-
14
15
end
16
Update I with gradient-based optimizer using Vol.
17
until convergence;
18
AW 0 Φ
19
Return: Fast PeRFlow fo and AW.
CFG-sync: We disable CFG by setting w 1 for d(zt, L4, 4,-1, c, w). The obtained PeRFlow model can use similar CFG scales as the pretrained diffusion models to guide the sampling.
w" for ( tk. - c, w) during training. The obtained PeRFLow model learns to straighten the specific ODE trajectories corresponding to (( fx. f C, w²). One should use smaller CFG scale (e.g., 1.0-2.5) adjust guidance when sampling from PeRFLow trained with CFG-fixed.
CFG-fixed: We use pre-defined
Through empirical comparison, we observe that PeRFlow+CFG-syuu preserves the sampling diversity of the original diffusion models with occasional failure in generating complex structures, while PeRFlow+ CFFGffxed trades off sampling diversity in exchange for fewer failure cases.
Our recommendations are as follows: When using powerful pre- preitrained diffusion models (c.g., SDXL) and prioritizing generation quality, PoRFLow+CFG is the better choice. On the other hand, when the goal is to maintain the sampling diversity and adaptability of customized fine-tuned plug-ins, such as Dreamshaper, PeRFLow++CF-ssyne is the more suitable option.
PeRFlow as Universal Plug-and-Play Accelerator PeRFlow initializes the weights of the student model with the pretrained diffusion model ó. After training with piecewise reflow, we find that the change of weights AW = 0 - & can be used to seamlessly accelerate many other flooflows pretrained with the diffusion model. For exmaple, AW of PeRFlow+4D-vI.5 can accelerate the ControlNets [52]. IP-Adaptor [49] and multiview generation [22] pipelines trained with the original SD v1.5. The accelerated pipelines achieve nearly lossless few-step generation as the original many-step generation. Please refer to Section 3.2 for detailed results.
Number of Time Windows The number of training segments depends on our expected minimum steps for the inference stage. Suppose the number of minimum steps for the inference stage is N, the number of training segments K should be less or equal to N. The reason that we cannot approximate the velocity of a time window by the velocity of its previous time window. So, for each window, we should allocate least one-step computation budget. This paper evaluates 4-step, 6-step, and 8-step generation capabilities, so we set the number of training segments as four. In some special cases (e.g., Wonder3D gigure Appendix), the trajectory across whole time window almost linear after 4-piece PeRFlow accelcration. We can generate multi-vien results with one step.
5

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But in most cases, we should use an inference step larger or equal to the training segments. On the computational cost, PeRFlow only requires the 1/K amount of steps for synthesizing the training target in each iteration, compared to that of InstaFlow.
3 Experiments
We use PeRFlow to accelerate several large-scale text-to-image and text-to-video models, including SD-v1.5, SD-v2.1, SIXL., and AnimateDiff. In this section, we will illustrate the experiment configurations and empirical results.
Experiment Configuration All the PeRFlow models are initialized from their diffusion teachers. PcRFlow-SD-vI.5 is trained with images in resolution of 512 x 512 using e-prediction defined in (7). PeRFlow-SD 1D-v2.1 is trained with images in resolution of 768 768 using e-prediction. PcRFlow-SDXL is trained with images in resolution of 1024 x 1024 using e-prediction defined in (8). Images are all sampled from the -AION-Assthttics-S dataset [37] and center-cropped. We also train PeRFlow-AA Fitloo--nnimteDiif with video clips in size of 16 x 384 x 384 using e-prediction defined in (8). We randomly drop out the text captions with a low probability (10%) to enable classifier- free guidance during sampling. We divide the time range [0, 1] into four windows uniformly. For each window, we use the DDIM solver to solve the endpoints with 8 steps. We refer to the Hugging Face scripts for training Stable Diffusion 2 to set other hyper-parameters. including learning rate and weight decay, All experiments are conducted with 16 NVIDIA A100 GPUs.
3.1 ste-step generation
PeRFlow succeeds in accelerating pretrained Stable Diffusion models to few-step generators. As shown in figure 2 and 3, PeRFlow can generate astonishing pictures with only 4 steps. If increasing the number of inference steps (e.g., 6), we can obtain images with much richer details. We compare the generation results with recent acceleration methods, including InstaFlow, LCM-LORA, and SDXL-lightning. PeRFlow enjoys richer visual texture and better alignment between text prompts and images. Refer to figure 10, 12, and 13 in Appendix for more results.
We compute the FID values of PoRFlow-acceleratee SDs in table using images three different [37], which is the training set of PcRFlow and other methods; (2) MS COCO 2014 [17] validation dataset; (3) images generated from SD- v1.5/XL with JourneyDB [41] prompts. We generate 30,000 images for the SD-v1.5 models and 10,000 for the SDXL series. We set the inference steps to 4 and 8 steps, respectively. In comparison to LCM-LoRA, we observe that PeRFlow models have obviously lower FID values. When increasing the number of inference steps, FID values of PeRFlow decrease because the numerical errors of solving ODE are better controlled. However, FID values of LCM-LoRA unexpectedly increase.
reference distributions: (1) LAION-5B-Aesthene
Domain shift caused by acceleration When accelerating diffusion models, expect preserve the performance and properties of the pretrained models. In table 1, we compute the FID values between the generation of the original SD models and the accelerated models. We observe the FID values of PeRFlow are smaller than LCM-LORA, InstaFlow, and SDXLL-Lghhnnig. This implies the distribution shift to the original SD models caused by PeRFlow is much smaller than other counterparts. The numerical comparison corresponds to the results in figure 5. The color style and layout of PeRFlow's results match the results of the pretrained models, while obvious domain shift appears in the results of LCM-LoRA, A. Besides, the sampling diversity of PeRFlow is similar to the original SD-v1.5 and appears to be better than LCMMLORA in figure 6.
3.2 PeRFlow as Universal Plug-and-Plas Accelerator on SD Work Flows
PeRFlow-AW serves as a universal accelerator that can be simply plugged into various pipelines trained on the pretrained Stable Diffusion models, including (but not limited to) ControlNet [52], IP-Adaptor [49], and multiview generation. For example, plugging PeRFlow-AW into the SD-v1.5 ControlNet-Tile gives a 4-step image enhancement module (figure 7). Combining this module with the 4-step SeRFlow-SD-vv.. we can generate high-quality 1024 x 1024 images with lightweight SD-v backbones. For multiview generation, plugging PeRFlow-AW AW into the Wonder3D [22]
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Base- Dase-DDIM&& 24 steps
LCM-LORA
4:5 steps
Lightning
steps
PeRFlow 4/ steps
Figure 2: The 1024 x 1024 images generated by PeRFlow enjoy richer details and better text-image consistency in comparison to other acceleration methods on SDXL. Prompt #1: "a closeup face photo of girl, wearing raincoat, in the street, heavy rain, bokeh "; Prompt #2: "a closeup face photo of boy in white shirt standing on the grassland, flowers"; Prompt #3: "a huge red apple in front of small dog, heavy snow". Prompt #4: "front view of boat sailing in cup of water".
Table FID values of different acceleration methods (lower values indicate better quality).
LAION-5B
COC02014
SD-v1.5
Method
4-step
8-step
4-step
8-step
4-step
8-step
InstaFlow
14.32
10.98
13.86
11.40
16.67
10.45
LCM-LoRA
15.28
19.21
23.49
29.63
15.63
21.19
PeRFlow
8.60
8.52
11.31
14.16
8,28
5.03
(a) SD-v1.5
LAION-SB
COC02014
SDXL
Method
4-step
8-step
4-step
8-step
4-step
8-step
Lightning
15.47
14.37
22.86
20.44
11.41
10.49
LCM-LoRA
13.66
13.31
19.74
21.70
9.42
9.90
PeRFlow
13.30
13.06
18.48
19.21
9.28
9.12
(b) SDXL
pipeline leads to one-step generation of multi-view images (figure 8). More results shown in figure 9.
3.3 Additional Discussion
Inference Budget Allocation PeRFlow divides the entire sampling trajectory into time windows it.. fx fx-1) with 1 = tk > > ty > f--1 > ... > to indicating noisy to clean states. After training, K K-step inference (one for each window) will yield high-quality images in most cases. However, for pictures with complex structures, such as motorcycles with well-crafted wheels and engines, PeRFlow may require more steps. Ho el al. [8] found that diffusion models generate images by synthesizing the layout and structure first and then refining the local details. We denote the
7

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Base-DDIM
steps
steps
stops
steps
Figure 3: The 512 512 images generated by PeRFlow enjoy richer details and color styles in comparison to other acceleration methods on SD-v1.5 (w/ DreamShaper). Images in each row are generated with the same random seed.
Figure 4: 6-step generation (16 512 512) via PeRFlow-Animatelo (motion module-v3 with DreamShaper). The text prompts used are "A young woman smiling, in the park, sunshine" and "A dog sitting in the garden, snow, trees".
number of inference steps by N. Inspired by this observation, first allocate each window with N//K steps. If N mod > 0, then the extra budget is given to time windows in noisy regions. Specifically, give one extra step for windows, whose index satisfies K < N mod K. In practice, PeRFlow creates 4 time windows for acceleration training, and 5-step inference consistently generates high-quality images.
Dynamic Classifier-Free Guidance CFG is useful technique to improve the layout, structure, and text alignment of the generated images. However, a large CFG scale sometimes leads to over-saturated color blocks [12, 43]. To mitigate this issue, we use dynamic CFG strategy for few-step sampling, ic.. the corresponding CFG scales decrease for window K to 1. For example, when sampling with

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(a) SD-v1.5
(b) PeRFlow
(c) LCM-LoRA
Figure 5: PeRFlow has better compatibility with customized SD models compared to LCM-LoRA.
The top is ErchitectureExterior and the bottom is DisneyPixarCartoon.
(a) SD-v1.5
(b) PeRFlow
(c) LCM-LORA
Figure 6: Three random samples from two models with the same prompts. PeRFlow has better sampling diversity compared LCM-LoRA.
steps, the CFG schedule is 7.5-4.0-4.0-4.0 for the CFG-sync mode and 2.5-1.5-1.5-1.5 for the CFG-fixed mode.
4 Related Works
Few-Step Diffusion Models Diffusion models have demonstrated impressive generative capabilities, but their iterative sampling process often suffers from slow inference speed [8, 39, 38.. To accelerate these models, various methods have been proposed. Progressive Distillation [35, 28] iteratively reduces the number inference steps to 4-8, but the error can accumulate during the process. Alternative approaches [45, 44, 54, 47, 16, 36] leverage adversarial losses to align the distributions and reduce the number of inference steps, but these methods often struggle with training instability and mode collapse. To avoid adversarial training, recent works [50, 30, 56] employ additional models to estimate the score of the generated data for distilling one-step generators, but this adds extra cost to the training pipeline. Consistency Distillation [40, 26] is novel pipeline for distilling few-step diffusion models by optimizing a consistency loss. However, the substantial difference between consistency models and the original diffusion models can hurt their adaptability pre- trained modules, In our work, PeRFlow provides simple, clean, and efficient framework for training few-step generative flows. By using different parameterizations as described in Section 2.2, PeRFlow achieves minimal gap with diffusion models, making it suitable for various pre- preitrained workflows.
Straight Probability Flows Learning straight probability flow a promising principle for obtaining fast generative flows [20, 19, 21, 4). Reflow is an effective way to learn such straight flows, but requires constructing large synthetic dataset [20, 21 which can introduce computational overhead and distribution shift. To avoid dataset construction. 46) use an extra neural network to estimate the initial noise corresponding an image, but training this network can be challenging. [33] employs mini-batch optimal transport to directly learn a straighter trajectory, but it is unclear how to apply this method conditional generation scenarios, such text-to-image generation. [29] finds the best step-size schedule for the pretrained generative model before reflow to improve efficiency, but cannot avoid dataset generation and the resulting distribution shift. PeRFlow provides a new method to avoid using synthetic datasets. It uses real training data to mitigate distribution shift and a devide-and-conoee strategy to efficiently perform reflow, leading to advanced few-step text-to- image generators. Sequential reflow[51] is concurrent work to ours. Compared to their work, we additionally provide different parameterization strategies to enhance the empirical performance in accelerating pre-traine traiteeied text-to-image models.

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Conclusions
In this work, we present Piecewise Rectified Flow (PeRFlow), a novel technique to learn few- step flow-based generative models. PeRFlow adopts divide-and-conquee strategy. separating the generation trajectory into intervals and applying the reflow operation within each interval. This yields two key advantages: (I) using real training data to mitigate distribution shift from synthetic data, and (2) avoiding the need to generate and store synthetic dataset prior to training. PeRFlow also designs proper parameterizations to inherit knowledge from pre-trained diffusion models for fast convergence. Consequently, PeRFlow accelerates powerful diffusion models like SD v1.5, SD v2.1, and SDXL., producing high-quality few-step image generators. Moreover, PeRFlow can be seamlessly combined with various SD workflows create their accelerated versions.
Limitations Currently, PeRFlow divides the time range into 4 windows, balancing inference and training costs. It needs 4 steps more for generation. To enable 1-2 step inference, we plan to explore multi-stage training and will focus on avoiding target synthesizing in the future.
Broader Impacts
This work proposes acceleration technique for generative models. can reduce the computational cost to less than 20% of the original and thus reduce the power cost. The proposed acceleration technique makes generative models more environmentally friendly.
Acknowledgment
The authors appreciate Yuanzhi Zhu for his valuable input and suggestions.
References
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Appendix
A More generation results
Table 2: Clip scores of different acceleration methods (high values indicate better quality). We select 5000 text prompts from COCO2014 and generate one image for each prompt for computing clip cosine similarity scores. PeRFlow's results align better with text prompts in comparison other methods.
Method
SDXL 25 steps
Lightning steps
LCM-LORA steps
PeRFlow steps
Score
0.337
0.330
0.327
0.337
Figure 4-step image enhancement (128 >> 1024) with PeRFlow-SD tiie [52]
Figure 8: One-step multiview generation of PeRFlow-SD Wonder3D [22]
Figure Fast generation via PeRFlow accelerated htwpd/eeepppe-Coooooooo [52]
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VIII
Figure 10: 4-step generation (512 x 512) via PcRFlow-SD-v1.5.
Figure 11: 8-step generation (512 x 512) via PeRFlow-SD-v..5
Figure 12: 4-step generation (768 x 768) via PcRF1ow-SD-v2.11
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Figure 13: 4-step generation (1024 X 1024) via PcRFlow-SDXL.
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Reviews:
[{"review_id": "9Cjipo7IGT", "reviewer": "Reviewer_ecCT", "summary": "The paper introduces a new flow-based method designed to accelerate diffusion models by dividing the sampling process into several time windows. The sampling path within each time window is straightened by the reflow operator. This approach allows for fast training convergence and, transferability, compatibility with various pretrained diffusion model workflows.", "questions": "- Can PeRFlow's approach be generalized to other types of generative models beyond diffusion models such as GAN-based or VAE-based?\n- Can you provide more detailed insights into the parameterization techniques used and their impact on the training convergence and final model performance?\n- What are the observed benefits of using synchronized versus fixed CFG modes?", "limitations": "N/A", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The approach’s motivation is clear. Theoretical arguments support the proposal well.\n- The empirical results are promising, and better than other existing baselines.", "weaknesses": "- When dividing the sampling process into several time windows, the error of the previous windows immensely affects the later ones, potentially increasing the cumulative error of the whole sampling process.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for the comments and advice.\n1. *When dividing the sampling process into several time windows, the error of the previous windows immensely affects the later ones, potentially increasing the cumulative error of the whole sampling process.*\n  - In practice, we observe increasing the number of time windows reduces the difficulty of training, because a shorter time window is easier to straighten and the error of this short window is better controlled.  \n  - We agree with this concern. This potential issue may happen when the error in each window does not change much concerning the time length. Then, more windows may lead to a larger error. But, in our experiments, we find the error of each time decreases obviously if we shorten the time window.\n\n2. *Can PeRFlow's approach be generalized to other types of generative models beyond diffusion models such as GAN-based or VAE-based?*\n  - GAN-based and VAE-based methods are naturally one-step generators. PeRFlow works well for iterative generators like diffusion/flow methods. \n\n3. *Can you provide more detailed insights into the parameterization techniques used and their impact on the training convergence and final model performance?*\n  - Pretrained diffusion methods learn much useful information from large-scale training data. Parameterizing the target few-step model in the same way as the pretrained diffusion helps inherit useful information, such as interacting with the conditioning texts. Then, the acceleration algorithm can train on a relatively small dataset and converge fast. \n\n4. *What are the observed benefits of using synchronized versus fixed CFG modes?*\n  - as discussed in section 2 (line 152-158), the CFG-sync mode preserves better the sampling diversity and the compatibilty of the original diffusion models with occasional failure in generating complex structures, while the CFG-fixed trades off these properties in exchange for fewer failure cases.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "CQKPD5QIWe", "reviewer": "Reviewer_FZ2P", "summary": "In this paper, the author proposes a new paradigm of sampling process (Piecewise Rectified Flow-PeRFlow) with reflow operation in the diffusion model, straightening the trajectories of the origin PF-ODEs and achieving a better performance in a few-step generation.\nSpecifically, the PeRFlow divides the sampling process (ODE trajectories) into multiple time windows, then does reflow operation in each single time window to straighten the trajectories in each time window. Compared to the original diffusion model with reflow operation, it significantly reduced the synthesis time of training data for reflow, also narrowing the numerical errors of solving ODEs when generating the training data to get a higher-quality generated training dataset. Also, it only requires several inference steps to solve the ending point in each time window, achieving a diffusion model acceleration method with faster training convergence, more linear trajectories, better performance.", "questions": "Please refer to the weakness part.", "limitations": "N/A", "rating": 7, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* The paper is well organized and clearly structured, it is very easy to follow.\n\n* Many fully detailed mathematical formulas are derived, making it easier to understand the details of the proposed method.\n\n* The figure about the proposed method is well designed, the effect and rough structure of the proposed method can be understood at a glance without looking at the text description.\n\n* The paper used enough large dataset of images which contain rich images & texts and used enough SOTA acceleration methods to evaluate the proposed method.", "weaknesses": "* The evaluation metrics for most generative models include FID and IS. And this paper only adopts the FID as the evaluation metric. Although this paper is aimed to accelerate the diffusion model with better performance, it is better if author can evaluate the diversity of generated images of the proposed method using the IS. In this case, people can know if such method will affect the diversity of generated images.\n\n* It would be better if author can directly indicate on the table that lower FID values are better. People who are not in the generative model filed are not familiar with FID.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for the comments and advice.\n\n1. *The evaluation metrics for most generative models include FID and IS. And this paper only adopts the FID as the evaluation metric. Although this paper is aimed to accelerate the diffusion model with better performance, it is better if author can evaluate the diversity of generated images of the proposed method using the IS. In this case, people can know if such method will affect the diversity of generated images.*\n  - Thanks for your suggestion. We will add the IS values in the final version. Due to the limit of rebuttal time and GPU resources, we cannot generate enough images to compute IS value in this round of discussion.\n\n2. *It would be better if author can directly indicate on the table that lower FID values are better. People who are not in the generative model filed are not familiar with FID.*\n  - Thanks for your suggestion. We will highlight this in the final version.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "ZWHoO9IYmk", "reviewer": "Reviewer_uqGM", "summary": "This paper presents a novel approach to accelerating diffusion models by introducing the Piecewise Rectified Flow (PeRFlow). This method significantly enhances the efficiency of generating high-quality generative samples by dividing the flow trajectories of diffusion models into several time windows and straightening them using a reflow operation.\n\nKey contributions of the paper include:\n- Superior Performance in Few-Step Generation: PeRFlow reduces the number of inference steps required while maintaining or improving the quality of generative samples.\n- Fast Training and Transfer Ability: The models adapt quickly due to inherited parameters from pre-trained diffusion models, demonstrating good transferability across different models.\n- Universal Plug-and-Play Capability: PeRFlow models serve as accelerators compatible with various pre-trained diffusion models, facilitating seamless integration into existing workflows.", "questions": "See the weakness above.", "limitations": "The authors have adequately addressed the limitations and potential negative societal impact of their work.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 3, "strengths": "Overall I find that the writing is clear, concise, and well-structured, making it easy for readers to follow the arguments and understand the key points. I like the idea of multi-step or piecewise generative models since it is natural to extend InstaFlow into a multi-step fashion, which offers flexibility between speed and quality.", "weaknesses": "- I think the multi-step consistency model [1] should be discussed since it has a strong correlation with this paper. In the experiments section, you only compare PeRFlow with LCM and InstaFlow, both of which are relatively early works. There are plenty of distillation methods in this field that are worth mentioning and comparing, including HyperSD [2], CTM [3], and DMD [4].\n- The most important hyper-parameter N, i.e., the number of segments, lacks analysis. How do you choose its value? What’s the relationship between the number of segments used in training and the number of sampling steps used in inference?\n- I like the idea of “plug-and-play” accelerator by extracting the delta weight to speed up other diffusion models. However, the implementation details and analysis in the paper are really limited with just a few demos. Besides, I think this is a general method that can be applied to any accelerated diffusion model, such as LCM?\n- The paper claims that “the computational cost is significantly reduced for each training iteration compared to InstaFlow”. However, do you have any quantitative evaluation, including the comparison with other methods?\n\n[1] Heek, Jonathan, Emiel Hoogeboom, and Tim Salimans. \"Multistep consistency models.\" ICML 2024.\n\n[2] Ren, Yuxi, et al. \"Hyper-sd: Trajectory segmented consistency model for efficient image synthesis.\" *arXiv preprint arXiv:2404.13686* (2024).\n\n[3] Kim, Dongjun, et al. \"Consistency Trajectory Models: Learning Probability Flow ODE Trajectory of Diffusion.” NeuIPS 2023.\n\n[4] Yin, Tianwei, et al. \"One-step diffusion with distribution matching distillation.” CVPR 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for the comments and advice.\n1. *I think the multi-step consistency model [1] should be discussed since it has a strong correlation with this paper. In the experiments section, you only compare PeRFlow with LCM and InstaFlow, both of which are relatively early works. There are plenty of distillation methods in this field that are worth mentioning and comparing, including HyperSD [2], CTM [3], and DMD [4].*\n  - Thanks for providing these related works. Yes, we add the discussion of [1], which shares a similar idea of dividing the whole time window into multiple segments. The difference is that [1] trains a consistency model for each segment while PeRFlow trains a linear flow.\n  - In Table 1, we compared PeRFlow with LCM, InstaFlow, and SDXL-lightning which is a state-of-the-art few-step text-to-image generator. Yes, we agree that other distillation methods should be discussed also.\n\n2. *The most important hyper-parameter N, i.e., the number of segments, lacks analysis. How do you choose its value? What’s the relationship between the number of segments used in training and the number of sampling steps used in inference?*\n  - The number of training segments depends on the minimum steps we expected for the inference stage.\n  - Suppose the minimum steps for the inference stage is N, the number of training segments K should be less or equal to N. In our experiments, we evaluate 4-step, 6-step, and 8-step generation results, so we set the number of training segments as four. \n  - The reason is that we cannot approximate the velocity of a time window by the velocity of its previous time window. So, for each window, we should allocate at least a one-step computation budget. \n  - In some special cases (e.g., Wonder3D in Figure 8 Appendix), after 4-piece PeRFlow acceleration,  the trajectory across the whole time window is almost linear. We can generate multi-view results with one step. But in most cases, we should use an inference step larger or equal to the training segments.\n\n3. *I like the idea of “plug-and-play” accelerator by extracting the delta weight to speed up other diffusion models. However, the implementation details and analysis in the paper are really limited with just a few demos. Besides, I think this is a general method that can be applied to any accelerated diffusion model, such as LCM?*\n  - Yes, the plug-and-play is a general property, like LCM, where we can add the delta-weights to any other diffusion pipeline for inference acceleration, such as controlnet, image-to-image, and ip-conditioned image generation.\n  - We should add more implementation details. The delta weights are equal to the weights after PeRFlow acceleration minus the initial pretrained weights.\n  - We provide a short analysis in line 196-204, where we observe that the delta-weights of PeRFlow can better preserve the properties of the original diffusion models in comparison to LCM, including a minor domain shift.\n\n4. *The paper claims that “the computational cost is significantly reduced for each training iteration compared to InstaFlow”. However, do you have any quantitative evaluation, including the comparison with other methods?*\n  - In each training iteration, the computational cost of PeRFlow for synthesizing the training target is $1/K$ of that of InstaFlow, where $K$ is the number of time windows. That's why we make the claim. \n  - For example, in each iteration, InstaFlow samples a noise and uses 32-step DDIM to solve the target ( solving from t=1 to t=0).  If PeRFlow divides the whole time window into 4 segments, it only requires 8-step DDIM operations to solve a sub- time window.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zey8tVUckQ", "reviewer": "Reviewer_FbPr", "summary": "This paper proposes piecewise rectified flow (PeRFlow) for accelerating pre-trained diffusion models. To overcome the requirement of synthetic data generation in rectified flow, the authors propose to prepare the training data by dividing the entire ODE trajectory into multiple time windows. The sampling trajectories within each time window are then straightened by the reflow operation. The proposed method is adapted to multiple diffusion models with different parameterizations. Experiments on text-to-image (SD-v1.5, SD-v2.1, SDXL) and text-to-video (AnimateDiff) models demonstrate the effectiveness of the proposed method.", "questions": "* The proposed method seems to be applicable to model training in addition to acceleration. Have the authors considered training their models from scratch on CIFAR-10 or ImageNet? This would allow a direct comparison of the performance/efficiency tradeoff with a broader family of flow matching algorithms.\n* What does \"one-step\" mean in Figure 8 when the sampling step should be lower bounded by the number of time windows of 4?", "limitations": "Yes. The authors have discussed their limitations in Section 5.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "* This paper addresses a major performance bottleneck in rectified flow, namely the synthetic data generation stage, which requires costly simulation with higher numerical errors. The proposed solution allows online simulation of ODE trajectories and thus more efficient training.\n* The proposed PeRFlow is extensively tested on multiple diffusion models for text-to-image and text-to-video generation, and the comparative results with the previous state-of-the-art few-step diffusion baselines are impressive.\n* Code is provided for both training and inference.", "weaknesses": "* The contribution of this work is weakened by its similarity to Sequential Reflow [1], and the additional design to be compatible with different parameterization strategies is somewhat incremental.\n* The main motivation to improve training efficiency (line 47) is not reflected in the experiments. The authors should provide a more comprehensive comparison with rectified flow in terms of performance/training computation tradeoff.\n* The statement in line 55 that PeRFlow \"has a lower numerical error than integrating the entire trajectories\" should be more carefully validated, e.g. by quantitatively comparing straightness [2] or curvature [3] within each time window. The authors could also apply their method to the commonly used 2D checkerboard data to provide a more intuitive visualization of the learned probability path.\n* There is a lack of ablation studies for several design choices. The authors should analyze the sensitivity of PeRFlow's performance to the number of time windows and sampling steps (more densely). It is also unclear how adding \"one extra step in $[t\\_K,t\\_{K-1}]$​\" (line 223) contributes to the final results.\n\n---\n\n1. Yoon, et al. Sequential Flow Straightening for Generative Modeling. arXiv 2024.\n2. Liu, et al. Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow. ICLR 2023.\n3. Lee, et al. Minimizing Trajectory Curvature of ODE-based Generative Models. ICML 2023.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you very much for the comments and advice.\n1. *The contribution of this work is weakened by its similarity to Sequential Reflow [1], and the additional design to be compatible with different parameterization strategies is somewhat incremental.*\n  - Technically, PeRFlow shares a similar idea of dividing a whole time range into multiple sequences. Moreover, PeRFlow designs dedicated parameterizations for each type of pretrained diffusion models, which facilitate fast convergence of acceleration. PeRFlow discusses the effect of CFG of teacher models during distillation. PeRFlow also demonstrates the plug-and-play properties of flow-based acceleration methods.\n\n2. *The main motivation to improve training efficiency (line 47) is not reflected in the experiments. The authors should provide a more comprehensive comparison with rectified flow in terms of performance/training computation tradeoff.*\n  - Yes, we agree that a more comprehensive comparison of performance/computation tradeoff should be included.\n  - In each training iteration, the computational cost of PeRFlow for synthesizing the training target is $1/K$ of that of InstaFlow, where $K$ is the number of time windows. That's why we make the claim. \n  - For example, in each iteration, InstaFlow samples a noise and uses 32-step DDIM to solve the target ( solving from t=1 to t=0). If PeRFlow divides the whole time window into 4 segments, it only requires 8-step DDIM operations to solve a sub- time window.\n\n3. *The statement in line 55 that PeRFlow \"has a lower numerical error than integrating the entire trajectories\" should be more carefully validated, e.g. by quantitatively comparing straightness [2] or curvature [3] within each time window. The authors could also apply their method to the commonly used 2D checkerboard data to provide a more intuitive visualization of the learned probability path.*\n  - Thanks for the advice, we should add some visualization. Usually, the claim may be held in most cases, because the accumulation error of numerical integration increases along with the length of time.\n\n4. *There is a lack of ablation studies for several design choices. The authors should analyze the sensitivity of PeRFlow's performance to the number of time windows and sampling steps (more densely). It is also unclear how adding \"one extra step in [𝑡𝐾,𝑡𝐾−1]\" (line 223) contributes to the final results.*\n  - Thanks for the advice. We will add more analysis in the final version. \n- number of time windows and sampling steps\n  - The number of training segments depends on the minimum steps we expected for the inference stage. Suppose the minimum steps for the inference stage is N, the number of training segments K should be less or equal to N. In our experiments, we evaluate 4-step, 6-step, and 8-step generation results, so we set the number of training segments as four. The reason is that we cannot approximate the velocity of a time window by the velocity of its previous time window. So, for each window, we should allocate at least a one-step computation budget. \n  - In some special cases (e.g., Wonder3D in Figure 8 Appendix), after 4-piece PeRFlow acceleration,  the trajectory across the whole time window is almost linear. We can generate multi-view results with one step. But in most cases, we should use an inference step larger or equal to the training segments.\n- We explain the inference budget allocation strategy in line 215-225. \n  - We agree it should be clarified with a more formal statement. Thanks for this suggestion.  Suppose we have $K$ time windows and $N>=K$ inference steps. From noisy to clean state, the time windows are indexed by $K, K-1, ... 1$.\n  - If N can be divided by $K$, each time window will be solved by $N//K$ steps. Otherwise, we allocate $N//K+1$ steps for windows, whose index $i$ satisfies $K-i < N \\text{mod} K$. The rest windows are allocated $N//K$ steps. In other words, we try to allocate the budget equally. If not divisible, the extra budget is given to time windows in noisy regions, because the important layout synthesis is finished in these regions.\n\n5. *The proposed method seems to be applicable to model training in addition to acceleration. Have the authors considered training their models from scratch on CIFAR-10 or ImageNet? This would allow a direct comparison of the performance/efficiency tradeoff with a broader family of flow matching algorithms.*\n  - In this work, we focus on the acceleration of pretrained diffusion models. We leave the study of pretraining (training flow models from scratch via PeRFlow) into future work. \n- Although Stable-diffusion 3 demonstrates that training a rectified flow (single-piece linear flow) can generate high-quality images, there are still several open questions to study. \n  - Piecewise linear flow generalizes the rectified flow, does there exist a proper window-dividing plan to train a better generation model?  \n  - If so, what kind of properties will it have in comparison to the vanilla rectified flow? Fast convergence? Fewer steps requested for inference sampling?\n\n6. *What does \"one-step\" mean in Figure 8 when the sampling step should be lower bounded by the number of time windows of 4?*\n  - Please refer to the answer to weakness 4.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: The paper presents a piecewise extension of rectified flows for accelerated sampling from diffusion models. The reviewers have acknowledged the quality of the presentation and the efficacy of the method on several datasets. However, they have also raised concerns regarding the novelty of the method in comparison to sequential flows and multistep consistency models. Given the new perspectives on different parameterizations and strong results, we are happy to recommend the paper for acceptance at NeurIPS.
Decision: Accept (poster)