Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow
Authors: Fu-Yun Wang
Ling Yang
Zhaoyang Huang
Mengdi Wang
Hongsheng Li
Venue: ICLR 2025 Poster (2025)
Keywords: Diffusion models
Rectified-Flow
Primary area: generative models

Abstract: Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its 
key components include: 1) using the linear interpolating diffusion form of flow-matching, 2) employing $\boldsymbol v$-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. 
Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

Published as a conference paper at ICLR 2025
RECTIFIED DIFFUSION: STRAIGHTNESS Is NOT YOUR NEED IN RECTIFIED FLOW
Fu- Yun Wang'
Ling Yang"
Zhaoyang Huang'
Mengdi Wang?
Hongsheng Li
MMLab, CUHK, Hong Kong SAR 2 Pekingg University, Beijing, China CPII under InnoHK, Hong Kong SAR fywang@1 ink, cuhk edu.kk, hk, yangl 8g08 1 80 63. com, drink incoddr @1 inkk www.kcckkkto edd..k mengdi wenpddiwprintttoo edu, hal i@ee. cuhk edu. hk
Princeton University, New Jersey, USA
ABSTRACT
Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving gen- erative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the linear interpolating diffusion form of flow-matching, 2) employing u-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the suc- cess of rectification primarily lies in using pretrained diffusion model obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) unnecessary. Further- more, we highlight that straightness is not an essential training target for rectifica- tion; rather, a specific case of flow-matching models. The more critical train- ing target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Dif- fusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g.. InstaFlow) but also achieves superior performance with even lower training cost. Our code is available httth:t::///......... //q wtw.uuu.oo//-----aaeao Rect fied-Di
INTRODUCTION
Diffusion models have greatly advanced the field of visual generation, enabling the creation of high-
quality images and vivid videos from text (Ho et al., 2020, Song et al.) 2020b Rombach et al.] 2022a Singer et al.] 2022. Podell et al.) 2023) Esser et al.) 2024 Shi et al. 2024). However, the generation process of diffusion models involves solving an expensive generative ODE numerically, which significantly slows down the generation speed compared to other generative models (e.g.. GAN) (Goodfellow et al. 2020 Sauer et al.) 2023b widely recognized solution to this issue rectified flow. The training target of rectified flow, highlighted in the previous works (Liu jet al. 2023 2022; Yan et al., 2024), is to make the new ODE path straighter, enabling the models to generate high-fidelity images with fewer steps while retaining the fiexibility of sampling with more inference steps for further quality enhancement. The key components rectified flow are threefold:
1) Flow-Matching, Rectified flow proposes to employ the linear interpolating diffusion form (Luu et al. 2022; Lipman et al. 2022), which is also known as flow matching form. The intermediate noisy state x; is defined as [1 - (_- where Xo is the clean data, e ~ No I) is normal noise, and & [0, 1] the timestep. This design more straightforward compared to the semi-linear form of the original DDPM (Ho et al. (2020).
2) v-prediction. Rectified flow proposes to adopt u-prediction (Salimans & Ho 2022 Liu al.)
2022). That is, the model learns to predict = Xg e. This makes the denoising form simple. For example, predict Xo based on x, with Xg X, têg, where 0 denotes the model

---

Published as a conference paper at ICLR 2025
Patred (Nolso, Image)
Training!
Efficient Flow Masching Modals
ODE grediction Ore-stap
Inpur
Rectified Flow
Models
Generate Data (ODE)
Rectified Diffusion (Ours)
Paired (Nolso, Image)
Simpler Stronger General
Find-Grder approcimate path (Curved or Stroight poth! Arbiteryy prodiction lype One-sttpg generation
Paired (Noive, Imagel
Training
Efficiant Diffusion Models
Figure 1: Overview of comparison between rectified flow and our rectified diffusion.
parameters and denotes the predictions. Moreover, it avoids the numerical issue when RJ 1 with e-prediction. For example, Xn-
X x xi=tée which is invalid.
3) Rectification. Rectification, also known as reflow, an important technique proposed in rec- tified flow (Liu et al. 2022). It is a progressive retraining technique that greatly improves the generation quality at low-step regime and maintains the flexibility of standard diffusion models. To be specific, turns an arbitrary coupling of Xo Po (real data) and in standard diffusion training to new deterministic coupling of &0 ~ IPg (generated data) and (pre-collected noise). To put it in a nutshell, it replaces the x, (1 ()x, + le with X, = (1- ttē where is real data, Xy is data generated by pretrained diffusion models 6, is the randomly sampled noise, and is the noise used to generate data Xg. Previous works em- phasize the rectification procedure is only feasible to e-prediction based flow- now-matching models. That is, they believe the first two points are the foundations to adopt rectification for improving efficiency. And they emphasize the rectification procedure 'straightens' the ODE path.
IP, (noise) adopted
The motivation of this paper is to investigate what is most essential about rectified flow. We ar- gue that the effectiveness of rectified flow stems from using a pretrained diffusion model to acquire matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs (i.e., the aforemennioned third point). Based on this, the aforementioned first two points (i.e., flow- matching & v- e-prrdiction) are unnecessary. This allows to generalize the design space of recti- fied flow and make it adaptable to various diffusion variants, including DDPM (Ho et al. 2020),
EDM (Karras et al. 2022). Sub-VP (Song al. 2020b), and etc.
To this end, we propose rectified diffusion, as illustrated Fig. [ our overall design is straightfor- ward. We keep everything of the pretrained diffusion models unchanged, including noise schedulers, prediction types, network architectures, and even training and inference code. The only difference that the noise e and data Xn adopted for training are pre-collected and generated by the pretrained diffusion models instead of independently sampled from Gaussian and real data datasets.
Additionally, we highlight that straightness no longer an essential training target when we gen- eralize the design space from solely linear interpolating diffusion form to more general diffusion forms. We analyze and show that the training target of rectified diffusion is obtain fider approximate ODE patl In simple terms, first-ordrr approximate ODE path implies the predic- tions of models remain consistent along the ODE trajectory and it still maintains the same ODE trajectory after each denoising step. For models like DDPM (Ho et al. 2020), the first-order ap- proximate ODE path inherently curved instead straight. Therefore, "straightness' is no longer suitable for rectified diffusion and is just special case when use the form of fow-matching.
It should be clarified that the "first-order approximate ODE path" in this paper is distinct from the traditional concept of "first-order ODE". In the conventional sense, first-order ODE does not include terms d'I such as स/ where n > 1. In this context, the ODE of general diffusion models is already "first-order ODE". However, our work, the "first-order approximate path" refers to an ODE with the property of heing immune high-order discretization emros.. This distinction will become clearer in later sections.
Note:
2

---

Published as a conference paper at ICLR 2025
1-step FID and CLIP Score of Rectified Diffusion over Training Iberationn
30.0
1-step FID of Rectified Diflusion
1-step CLIP Score of Rectified Diftusion
1-step FID Rectified
1-step Score Rectifted
29.5
45
29.0
40
28.5
CLIP
35
28.0
30
27.5
27.0
25000
75000
100000
125000
15000D 175000
200000
Training Iterations
Figure 2: Training iterations. 1-step performance of rectified diffusion significantly surpasses the 1-step performance of rectified flow within only 20,000 iterations with batch size 128 (only 8% trained images of rectified flow) and consistently grows with more training iterations. The dashed lines represent the final performance of the rectified flow (Liu al. 2023). Since the training code of rectified flow (Liu et al. 2023) is not open-sourced, intermediate metrics cannot be tested.
To empirically validate our claim, we conduct experiments using Stable Diffusion, comparing our approach with InstaFlow (Liu et al. (023). key baseline based on rectified flow for text-to-image generation. We adhere to the training setting of InstaFlow. The primary distinction is that In- staFlow requires transforming the Stable Diffusion into u-prediction flow-matching model, while our method leaves everything of the original Stable Diffusion unchanged. Our results demonstrate apparently better performance and faster training, likely due to minimal differences in diffusion configurations. Our one-step performance achieves significantly superior performance with only 8% trained images of InstaFlow shown in Fig. -
Besides, we propose to replace the second-stage distillation adopted in InstaFlow with consistency distillation. We observe that the first-order approximate ODE path greatly facilitates consistency distillation, allowing us to achieve better performance at 3% the GPU days than the further distilled model of InstaFlow. Additionally, we introduce rectified diffusion (Phased), which divides the ODE path along the time axis into multiple segments and enforces first-order approximate ODE paths within each segment. While this segmentation increases the minimum number of generation steps to match the number of segments, it substantially reduces both training costs and time. When compared to the previous segment- based rectified flow method, PeRFlow (Yan et al. 2024), our approach demonstrates significantly better performance in experiments conducted Stable Diffusion v1- 5 (Rombach et al., 2022a) and Stable Diffusion XL (Podell et al.) (023).
We summarize main contributions follows: (i) We conduct an in-depth analysis of the essence of rectification and extend rectified flow to rectified diffusion. (ii) We identify that it is not straight- ness but first-order approximate ODE path is the essential training target of rectified diffusion. (fii) Comprehensive comparisons on rectification, distillation, and phased OED segmentation demon- strate our method achieves superior trade-off between generation quality and training efficiency over rectified flow-based models.
2 RECTIFIED DIFFUSION: GENERALIZING THE DESIGN SPACE OF RECTIFIED FLOW INTO GENERAL DIFFUSION MODELS
Rectified flow is subset of rectified diffusion. In the following discussion, apply the general diffusion form Kingma et al. 202I) X, = a,X9 + o,E to introduce rectified diffusion. Note that this form of diffusion covers the flow-matching since we can simply ot 1 and a, Con-
3

---

Published as a conference paper at ICLR 2025
sidering the different prediction types, apply the epsilon-prediction for the following discussion. But note that different prediction types can be converted effortlessly through re- paramettrrizaiion. For Xa -n-rrcdcctoo,,
have Xn
X.= For u-prediction utilized in rectified flow, we have de
X - X=- =a-(atto.) Hence, we claim that rectified flow is subset of rectified diffusion, and rectified diffusion is generalization of rectified flow.
oe
2.1 THE NATURE OF RECTIFICATION IS THE RETRAINING WITH PRE-COMPUTED HOISE-SAMPLE PAIR
The secret of rectification is using paired noise-sample for training. To illustrate the differences clearly, we visualize the training processes for standard flow matching and rectification (reflow) training, as described in Algorithm D and Algorithm 3 respectively. Differences are highlighted in red. A key observation is that in standard flow matching training, Xo represents real data randomly sampled from the training set, while the noise e is also randomly sampled from Gaussian. This results in random pairing between noise and sample. In contrast, rectification training, the noise is pre-sampled from Gaussian, and the images are generated using pre-sampled noise by the model from the previous round of rectification (the pre-trained model), leading to a deterministic pairing.
Flow-matching training (with linear interpolating form) is subset of standard diffusion train- ing. In addition, Algorithm 2 visualizes the training process of more general diffusion model, with differences to Algorithm| I highlighted in blue and orange. It's important to note that flow matching a specific case of the diffusion forms we discuss. From the algorithms, it is evident that the only distinctions between them lie in the diffusion form and prediction type. Consequently, flow match- ing training with linear interpolating form is just a special case of general diffusion training under a particular diffusion form and prediction type.
By comparing Algorithms 2 and B with Algorithm I it is straightforward to derive Algorithm Essentially, by incorporating the pre-trained model to collect noise-sample pairs and replacing the randomly sampled noise and real samples with these pre-collected pairs the general diffusion training, we obtain the training algorithm for rectified diffusion.
Algorithm Flow Matching v-Prediction
Algorithm 2 Diffusion Training E-Prediction
Input:
Input: dgg dz
Sample Xy from the data distribution
Sample Xy from the data distribution
Sample time / from a predefined schedule or uniformly from [0,
Sample time l from a predefined schedule or uniformly from [0, 1]
Sample noise from normal distribution
Sample noise from normal distribution
Compute X2 X2 (1-t) t) Xg +
Compute x; X, = 04 Xg + o;
Predict velocity i using the model: 0
Predict noise é using the model: é
Model(x,, t)
Model(x;, t)
Compute loss: L || (xg 1
Compute loss: L= || cl2 Backpropagate and update parameters
Backpropagate and update parameters
Algorithm 3 Rectified Flow v- p-Prediction
Algorithm 4 Rectified Diffusion e- c-Prrdiction
Input: noise-data pair (e, Xx)
Input: noise-data pair (e, &o), Otz, de Sample-x, frem the-tatetttt distribution Sample time from a predefined schedule or uniformly from [0,
Sample from-tte--laee elat distribution
Sample time from predefined schedule or uniformly from [0, 1]
Sample noise from normal distribution
Gample-neise e. frem-rfrmmmettee normal distribution connrn-nnnnld-issiiitttttoo
Compute x4 = (1 tt -
Compute X, = ox
Predict velocity using the model: à
Predict noise using the model: é Model(x,,
Model(xe, !)
Compute loss: 1
Compute loss: L = I|e - ell
Backpropagate and update parameters
Backpropagate and update parameters
4

---

Published as a conference paper at ICLR 2025
2.2 UNDERSTANDING THE HIRST-ORDER APPROXIMATE ODE PATH (* x)
How do we define a first-order approximate ODE path, and what are its requirements? For the above discussed general diffusion form X Xx o,E, there exists an exact ODE solution form (Lu et al. 2022).
dr E (x(e, Oit
0t:
X2
(1)
where X In o1 and 1x is the inverse function of X, As indicated in previous work (Kingma et al. 2021), A should be a monotonically decreasing function. The left term _ X, a pre-defined deterministic scaling. The right term the exponentially weighted integral of epsilon predictions. The first-order approximate ODE path means the above integral with arbitrary t and is equivalent to
o,
0t x, CG (X,, 0,
0t x, (x azs
e
dx
Ot
We show that the equivalent of Equation T and Equation 2 for arbitrary t and s holds and only holds if the epsilon prediction the same ODE trajectory is constant in Thereom T
What is the principle behind the first-order approximate ODE path? The equivalence between Equation and Equation does not generally hold across most cases. Specifically, as a first-order Taylor series approximation of Equation as f(s t). Their relationship can then be written as:
Se I Let's assume the outcome of Equation
represented as fs, t) and that of Equation 2
f(s () [ss () + o())-))))).
Widely adopted ODE solvers in the community, such DDIM and the Euler solver, operate under the premise that Equation D and Equation 2 are interchangeable, thus disregarding the higher-order error terms. These terms, denoted leading to issues when the gap A A grows significant. This explains why DDIM necessitates minimum of 50 steps to produce high-quality results. By contrast, our work sidesteps such ap- proximations. Our key aim is to enhance the PF-ODE to guarantee first-order accuracy, eliminating higher-order error terms via a paired retraining approach (rectificationn. This underpins why Recti- fied Diffusion achieves high-quality generation in a single step.
O(A), - ),) are typically overlooked during inference,
Why rectified diffusion leads to a first-order approximate ODE path? Suppose the ODE trajec- tory is already first-order approximate ODE path with solution point Xp. We define the constant epsilon prediction along this ODE trajectory e. Substituting s 0, Xg, ag o 0, and into Equation 2 we obtain:
0t Xo + arE
Øz -t - ai + OrE.
=a,x0
(4)
This matches the structure of the predefined forward process precisely. Hence, the first-order ap- proximate ODE path represents a weighted blend of data and noise, aligning with the predefined forward diffusion framework. The difference, however, is that in this equation, and xo are de- terministic pair tied to the same ODE trajectory, while in standard diffusion training, Xo and e are sampled randomly.
Now, if we achieve perfect coupling between the noise e and data Xa during training and ensure the no-intersection condition holds, x, will correspond unique noise-data pair. In the absence of optimization errors, this leads to:
Xx a.Xo
6
80 Xx, *x
Vx, log PP(x Xo) =
(5)
of
Given that cø -0.80, it follows that the epsilon prediction along the PF-ODE will consistently this implies that we successfully recover the first-order
equal e. Referring back to Theorem [ approximate ODE path.
This indicates that, with perfect pairing of the data X, and noise e during training, and provided there overlaps between distinct paths (which could otherwise result in epsilon predictions averaging
5

---

Published as a conference paper at ICLR 2025
KDM
100M
1.4
0.1
(a) Flow Matching
(b) EDM
(c) DDPM
SupA7P
Trandiendd Corw
1X
1.2
80 02
041
0.3
14
-10
056
8.00
1.3
142
1.44
(d) Sub-VP
(e) Transformed
Figure 3: First-order approximate ODE paths of different diffusion forms. We show that the first- order approximate ODE path has the same form as their predefined forward process, i.c., x = a,x0 Though the first-order approximate ODE paths of Flow Matching and EDM are straight, the first-order approximate ODE paths of DDPM and Sub-VP are inherently curved. First-order approximate ODE paths of all diffusion forms can be converted into straight lines through simple scaling as shown in Fig. 3e
over multiple paths), diffusion model trained under ideal conditions (without optimization errors) would yield the first-order approximate ODE path. Indeed, as indicated by previous work (Lee) al. 2024), the probability of overlaps between distinct paths is actually close to zero with only once rectification. Additional insights are provided in the supplementary Section IV
First-order approximate ODE path supports consistent generation with arbitrary inference steps. Additionally, note that the epsilon predictions on the same trajectory are constant, it is easy to show that the Xo-predictions also constant. Therefore, the first-order approximate ODE path can flexibly support one-step generation (X, + x6) or multi-step generation (Xy + - x,)- If perfect first-order approximate ODE path is achieved, we will always get identical generation results with arbitrary inference steps.
First-order approximate ODE path be inherently curved. For the first-order approximate ODE path, though the trajectories of flow-matching based methods are straight, the trajectories of other forms of diffusion models can be inherently curved. We showcase our findings in Fig. We select X₂ = [0. 1] and
[1. 1] The Fig. aaland Fig. (b) sboshow the first-order approximate ODE paths of flow- now-matching and EDM. They are both straight, but EDM has a totally different trajectory and magnitude. Fig. 3c and Fig. 3d show the first-order approximate ODE paths of DDPM and Sub-VP. Their first-order approximate ODE paths are inherently curved. But we define ye S; we will have y: = _ + from the Equation We can easily observe that the trajectory of y: is straight line from the initial point towards the direction x (i.e, first-order trajectories can converted to straight lines). Fig. 3el shows the trajectory of yr = 2t e. It shows that all the first-order trajectories can be converted into straight lines with simple timestep-depender scaling.
2.3 RECTIFIED DIFFUSION (PHASED)
Completely smoothen the ODE path of a pre-trained diffusion model into first-order approximate ODE path challenging because the original ODE can deviate significantly from the target ODE. In Fig. 4 we visualize both the original diffusion ODE path and the corresponding first-order ap- proximate ODE path. Since it's hard to intuitively determine whether a curved ODE path satisfies represent the first-order approximate ODE path with straight line. A significant gap between the two paths is evident. However, enforcing local first-order approximate ODE path is more feasible. As shown on the right side of the figure, when the ODE path is divided into two seg-
the property,

---

Published as a conference paper at ICLR 2025
Dau
No06 pretralned diffusionn models
trajectory
trajectory rectified diffusion models
trajectory of phased rectified diffusion
Figure 4: ODE trajectory comparison of diffusion models, rectified diffusion models, and phased consistency models. Since it's hard to visually tell whether a curved ODE path satisfies first-order property,we apply straight lines for more clear demonstration. The solid line shows the original diffusion ODE path, while the dashed line shows the rectified ODE path.
ments along the time axis and each segment is smoothened separately. the new ODE path is closer to the original one. This observation motivates the development of our rectification diffusion (phased).
0 < < 82 < ... 8M-- = mmx along the time axis the number of phases. The training process begins with sampling Xg from real data, followed by adding random noise at time step 8m obtain Xs... We then use the pre- trained diffusion model to perform multi-step numerical solving to obtain X for the previous intermediate step. However, the phasing idea involves two challenges: 1) determining the noise corresponding to the first-order approximate ODE path, and 2) determine the sample x, at any time t between 8m and 8m-1 the same first-order approximate ODE path, where t E (8m-1, 8m )- Fortunately, the transition formula between any two points on the first-order approximate ODE path is known, shown in Equation 2 Through a simple transformation, have the noise corresponding to the ODE path between Xsm.. and X can be expressed as:
We set intermediate time steps as of ODE, where
Xam-1
Xem
Az ANSR
m-m-1
0xm=1
Gay
Drm-1
Clem
where Az represents the change in 2, and ANSR denotes the change in da de Once this noise is caleulated, it can be directly substituted into Equation 2 to compute x, at any time f along the ODE path.
At first glance, might think that rectified diffusion (phased) is similar to the phased consistency model and related trajectory distillation methods However, they differ in scope and application scenarios. From technical perspective, although the learning objective for both is compute the solution point for each segment, the construction of their inputs differs. For the phased consistency model, the sampled points still lie on the original PF-ODE trajectory, whereas rectified diffusion (phased), the sampled points are constructed based on the properties of the first-order approximate ODE path as discussed above. terms of application scenarios, the phased consistency model is limited by the constraints of the consistency model itself; to achieve deterministic multi-step inference, it typically requires training separate model for each multi-step scenario. In contrast, rectified diffusion (phased) can theoretically enable deterministic inference for any number of steps (greater than a preset number of steps).
2.4 RECTIFIED DIFFUSION FACILITATES THE CONSISTENCY DISTILLATION
Previous work (Luu et al. 2023) proposes applying naive distillation after rectification to enhance one-step generation ability. This is because, after rectification, the model cannot achieve perfect first-order path due to issues like optimization, model capacity, and ODE path intersections. As a result, rectified flow-hased methods still do not perform well the most advanced distillation

---

Published as a conference paper at ICLR 2025
ODC branctery and predittor of model
OTE ecteyy and pre Bitten consileenyy
D01 Pndector and anoeichand reckiied Votonn
(a) Diffusion models
(b) Consistency models
(c) Rectified diffusion (Ours)
Figure 5: ODE trajectory and prediction comparison of consistency models and reftified diffusion. Since it's hard to visually tell whether a curved ODE path satisfies first-order property,we apply straight lines for more clear demonstration. The yellow line shows the ODE trajectories, while the blue line shows the predictions.
F1D vs. CLIP Score (1 step)
FID vs. CLIP Score 12 step)
PID vs. CLIP Score 16 step)
FID vs. CLIP Score (8 step)
60-
Bectilied Dillussn llactitted Flew
Beckdied Ditivasco --- Blattiteed Elow
Rectdied Diilatioo
25.5
Rectaled Dillwiiss Reectiieed flow
Rechitee Flow
25.0
70
60-
40
24.0
28
28.0
30-
24-
30
25-
25
27
28
25
22
30
51
22
30
31
50.0
36.5
31.0
$1.5
CLIP Score
CLUP Scom
CLIF Scome
CLIP Score
Figure 6: Effectiveness of Classifier-Free Guidance. The CFG values are 1, 1.2, 1,5, 2.0 respectively. By default, we adopt CFG value 1.5 for both rectified diffusion and rectified flow. Proper CFG values can significantly improve the performance even in one-step generation.
methods at low-step regime (e.g., 1-step generation). Following it, we also utilize distillation to fur- ther improve the model's performance at low-step regime after rectified diffusion. Instead of using naive distillation, we employ the more advanced distillation technique sechiqqe--consistency distillation (Song et al. (023), which eliminates the need to regencrate large numbers of samples. Moreover, found that after rectification, where the ODE path is close to the first-order approximate ODE path, con- sistency distillation leads to significantly faster training and better performance. This is because the training objective of a first-order approximate ODE path imposes a stronger constraint than self- consistency, In Fig. 5 we illustrate the differences between the diffusion model, consistency model, and rectified diffusion. The consistency model only adjusts the direction of the model's predictions without altering the ODE path itself, while rectified diffusion enforces change in the ODE path.
EMPIRICAL VALIDATION
3.1 VALIDATION SETUP
To thoroughly compare our approach with rectified flow-based methods, we organize the comparison into three levels:
1) Rectification comparison: InstaFlow (Liu et al. 2023) proposes initializing a v-prediction- based flow-matching model using Stable Diffusion vI-5 (Rombach et al., 2022a), followed by further training with their rectified flow method, which we refer to as Rectified Flow. To com- pare with this, we apply the rectified diffusion method continue training Stable Diffusion v1-5, referred to as Rectified Diffusion. This comparison aims to demonstrate the faster training speed and superior performance of our proposed rectified diffusion approach.
2) Distillation comparison: In the InstaFlow paper, the authors suggest using a standard distilla- tion technique to improve the model's performance in a one-step scenario, which we refer to as Rectified Flow (Distill). Similarly, we apply a distillation strategy to enhance performance
8

---

Published as a conference paper at ICLR 2025
at low-step regimes, specifically using consistency distillation to boost training efficiency. This approach is termed Rectified Diffusion (CD).
3) Phased ODE segmentation: PeRFlow Yan al. 2024 introduces the concept segmenting
the ODE and presents experimental results on both SD and SDXL (Podell et al. 2023). termed PeRFlow and PeRFlow-XI,, respectively. We extend this idea by proposing a method for phasing the ODE to enforce first-order property within each sub-phase, which we call Rectified Diffusion (Phased) and Rectified Diffusion-Xi (Phased).
Across all three of these comparative experiments, our methods demonstrate significantly superior performance.
Table 1: Performance comparison validation set of COCO-2017.
Method
Res.
Time
Steps
Param.
FID ())
CLIP
SDv1-54DPMSolver (Upper-Bound) Bound) al. 2022
Rectified Flow LLu ct al.
2023
0.88s
0.9B
21.65
0.315
Rectified Flow
512
0.09s
0.9B
47.91
0.272
Rectified Flow LLu ct 2025
512
0.13s
2
0.9B
31.35
0.296
Rectified Diffusion (Ours)
512
0.88s
25
0.9B
21.28
0.316
Rectified Diffusion (Ours)
0.09s
0.9B
27.26
Rectified Diffusion (Ours)
512
0.13s
22.98
0.309
Rectified Flow (Distill) Liu 2023
0.09s
0.302
Rectified Flow (Distill)
512
0.133
2
0.98
73.49
0.261
Rectified Flow (Distill) Liu af 2025
512
0.21s
0.9B
103.48
0.245
Rectified Diffusion (CD) (Ours
0.09s
0.98
22,83
0.305
Rectified Diffusion (CD) (Ours)
512
0.13s
21,66
0.312
Rectified Diffusion (CD) (Ours)
512
0.21s
0.9B
21.43
0.314
PeRFlow Yan et al. 2024
512
0.21s
4
0.98
22.97
0.294
Rectified Diflusson (Phase)) (Ours)
512
0.21s
0.9B
20.64
0.311
PcRFlow-SDXL Yun al.
2024
1024
0.71s
4
3B
27.06
0.335
Rectified Diffusion-SDXL (hased) (Ours)
1024
0.71s
3B
25.81
0.341
Xrbiom
(a) I-step comparison
(b) 2-step comparison
(c) 4-stop comparison
(d) Phased (4-step)
(e) Distillation (1-step)
Figure 7: Human preference metries comparison.
3.2 COMPARISON
Training cost. Following the setup from the InstaFlow paper, we first use Stable Diffusion v1-5 and DPM-Solver (Lu et al.) 2022 to generate 1.6 million images. Since InstaFlow does not specify the prompts used, we generate images using a randomly sampled set 1.6 million prompts. During the training of Rectified Diffusion,
used batch size of 128 for total of 200,000 iterations, resulting in total of 128 x 200, 000 = 25, 600, 000 samples processed. In comparison, InstaFlow processed 64 x 70, 000 1024 x 25, 000 30, 080, 000 samples. Thus, our total training cost is lower than that

---

Published as a conference paper at ICLR 2025
of InstaFlow. Additionally, InstaFlow's total training time 75.2 A100 GPU days, whereas method required approximately 20 A800 GPU days. Typically, the training efficiency of an A800 is about 80% of that of an A100. We attribute this significant reduction in training time to not using the LPIPS Loss (Zhang et al. 2018), which generally improves FID but incurs substantial memory and computational costs during the latent diffusion decoding process. For the second-stage distillation, we employ consistency distillation training with a batch size of 512 for 10,000 iterations, consuming total of 4.6 A800 GPU days. In contrast, the distillation process described in the InstaFlow paper takes 110 A100 GPU days. Our training cost is approximately 3% of the GPU days of InstaFlow's s distillation process.
Training speed. We monitor the performance of Rectified Diffusion in terms of FID and CLIP score at different stages of training. was observed from Fig. 2 that our method achieve superior one-step performance compared to Rectified Flow after just 20,000 iterations, with further signifi- cant improvements as training continued. At this stage, the number of samples processed was only about 8% of the samples processed by Rectified Flow. This efficiency is largely because Rectified Diffusion does not require converting the original epsilon prediction diffusion model, which fol- lows the DDPM form, into v-prediction flo-matchhing model a process that incurs significant computational cost.
Qualitative comparison. We present comparison of the images generated by Rectified Diffusion and Rectified Flow across various scenarios in Fig. g and Fig. 9 First, we can observe that the Rectified Flow model performs poorly at low step counts, producing only very blurry images in fewer than eight steps. Additionally, we notice that the images generated by PeRFlow are blurry and fail to reflect the content of the text. Moreover, the results generated by Rectified Flow (Distill) remain relatively blurry and lack the ability for multi-step refinement, which limits its applicability. Rectified Diffusion shows clearly superiority in these settings.
Quantitative comparison. We calculate the FID (Heusel et al. 2017 and CLIP scores (Radford (tt al.] 202T) for different models on the COCO-2017 validation set (Lin et al. 2014) and the 30k subset of the COCO-2014 validation set (Lin et al. (014),, respectively. As shown in Table and Table 3 our model consistently outperforms the methods based on rectified flow across both met- rics, different scenarios, and various steps. It also achieves performance comparable to advanced distillation and GAN training methods.
Human preference metrics. To more comprehensively evaluate the model performance, we compare the outputs using human preference models. We follow the testing sctup of Diffusion- DPO (Wallace et al.; 2024), generating images with 500 unique prompts from the Pick-a- pic (Kirstain et al., (023) validation set for comparison. We used the Laion-Aesthetic Predic- tor (Schuhmann] 2022), Pickscore (Kirstain al. 2023), HPSv2 (Wu et al. 2023), and ImageRe- ward (Xu et al. (024a) to score the generated results from each model individually and calculate the win rate of each model across these metrics. Our results, shown in Fig 7 consistently outperform the results of rectified flow-based models.
CFG-influence. We show the performance comparison of FID and CLIP Score between Rectified Flow and Rectified Diffusion under different step counts and CFG values in Fig. 6 We observe that Rectified Diffusion consistently outperforms Rectified Flow, especially in the low-step regime. Additionally, we find that CFG has significant impact on both Rectified Diffusion and Rectified Flow; even in the 1-step generation scenario, using an appropriate CFG value can still significantly enhance performance. The CFG values are 1, 1.2, 1.5, 2.0 respectively.
4 CONCLUSION
In conclusion, we rethink and investigate the essence of rectified flow. We demonstrate that retrain- ing with pre-collected noise-image pairs is the most important factor. Building on this insight, we propose Rectified Diffusion, extending its scope to general diffiusion forms. We identify that it is not straightness but first-order property is the essential training target of Rectified Diffusion. Ad- ditionally, by incorporating consistency distillation and introducing Rectified Diffusion (Phased), further enhance training efficiency and model performance, offering streamlined approach to efficient high-fidelity visual generation. Vast validation demonstrates the advancements of Rectified Diffusion.
10

---

Published as a conference paper at ICLR 2025
ACKNOWLEDG
This project is funded part by National Key R&D Program of China Project 20222D0161 100, by the Centre for Perceptual and Interactive Intelligence (CPII) Ltd under the Innovation and Technol- ogy Commission (ITC)'s ' InnoHK, by NSFC-RGC Project N. N.CCHK498/24, Hongsheng Li is a PI of CPII under the InnoHK.
REPRODUCIBILITY STATEMENT
We have undertaken substantial efforts ensure that the results in this paper are reproducible. The training and evaluation code, along with detailed guidance, is made available at https: Additionally, we have released the pre- co/ wwwg /Rect f ed ffus' on Sreeciffee-DD
com/ cwt.commmmmm// htt.:////.--A/eeeeeeeeeeeeaaaaaa
trained weights at hnttps://hugginggfan We believe these resources will aid replicating our findings and foster further research that builds upon our contributions.

---

Published as a conference paper at ICLR 2025
REFERENCES
Michael S Albergo and Eric Vanden-Fijnden. Building normalizing flows with stochastic inter- polants. arXiv preprint arXiv:2209. 2022.
Michael S Albergo, Nicholas M Boffi, and Eric Vanden-Fijnden, Stochastic interpolants: A unifying framework for flows and diffusions. arXiv preprint arXiv:2303.08797 2023.
Yogesh Balaji, Scungjun Nah, Xun Huang, Arash Vahdat, Jiaming Song, Qinsheng Zhang, Karsten Kreis, Miik Aittala, Timo Aila, Samuli Laine, et al. ediff-i: Text-to-image diffusion models with an ensemble of expert denoisers. arXiv preprint arXXiv2221..0 1.01324, 2022.
Huiwen Chang, Han Zhang, Jarred Barber, Aaron Maschinot, Jose Lezama, Lu Jiang, Ming-Hsuna Yang, Kevin Patrick Murphy, William T. Freeman, Michael Rubinstein, Yuanzhen Li, and Dilip Krishnan. Muse: Text-to-image generation via masked generative transformers. In Andreas Krause, Emma Brunskill, Kyunghyun Cho, Barbara Engelhardt, Sivan Sabato, and Jonathan Scarlett (eds.). ICML, volume 202 of PMLR, pp. 4055-4075. PMLR, 23-29 Jul 2023. URL https::/proceedings mlr www.ppresssseee
/tcess/v200 w220//22222///// httpo//ccaaagb..cc hb.tmml
Soravit Changpinyo, Piyush Sharma, Nan Ding, and Radu Soricut. Conceptual 12m: Pushing web- scale image-text pre-training recognize long-tail visual concepts. In CVPR, pp. 3558-3568, 2021.
Minshuo Chen, Kaixuan Huang. Tuo Zhao, and Mengdi Wang. Score approximation, estimation and distribution recovery of diffusion models on low-dimensional data. In International Conference on Machine Learning, pp. 4672 4712. PMLR, 2023.
Minshuo Chen, Song Mei, Jianqing Fan, and Mengdi Wang. Opportunities and challenges of diffu- sion models for generative ai. National Science Review, I1(12):nwa3348, 2024.
Ricky TQ Chen and Yaron Lipman. Riemannian flow matching general geometries. arXiv preprint arXiv:2302.0366/ 2023.
Prafulla Dhariwal and Alexander Nichol. Diffusion models beat gans image synthesis. NeurIPS, 34:8780-8794, 2021.
Ming Ding, Zhuoyi Yang, Wenyi Hong, Wendi Zheng, Chang Zhou, Da Yin, Junyang Lin, Xu Zou, Zhou Shao, Hongxia Yang, et al. Cogview: Mastering text-to-image generation via transformers. NeurlPS, 34:19822-19833 2021.
Patrick Esser, Sumith Kulal, Andreas Blattmann, Rahim Entezari, Jonas Müller, Harry Saini, Yam Levi, Dominik Lorenz, Axel Sauer, Frederic Boesel, et al. Scaling rectified flow transformers for high-resolution image synthesis. arXiv preprint stXiv:2403.03206 2024.
Oran Gafni, Adam Polyak, Oron Ashual, Shelly Sheynin, Devi Parikh, and Yaniv Taigman. Make-a- scene: Scene-based text-to-image generation with human priors. In ECCV, pp. 89-106. Springer, 2022.
Zhengyang Geng, Ashwini Pokle, William Luo, Justin Lin, and J Zico Kolter. Consistency models made easy. arXiv preprint arXiv:2406. 14548, 2024.
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial networks. Communications of the ACM, 63(11):139-144, 2020.
Jiatao Gu, Shuangfei Zhai, Yizhe Zhang, Lingjie Liu, and Joshua M Susskind. Boot: Data-free distil- lation of denoising diffusion models with bootstrapping. In ICML 2023 Workshop Structured Probabilistic Inference { Generative Modeling, 2023.
Yingqing Guo, Hui Yuan, Yukang Yang, Minshuo Chen, and Mengdi Wang. Gradient guidance for diffusion models: An optimization perspective. Advances in Neural Information Processing Systems, 37:90736-90770, 2025.
12

---

Published as a conference paper at ICLR 2025
Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. NeurIPS, 30, 2017.
Jonathan Ho, Ajay Jain, and Pieter Abbeel. ddpm. NeurIPS, 33:6840-660 68511, 2020.
Minguk Kang, Jun- Yan Zhu, Richard Zhang, Jaesik Park, Eli Shechtman, Sylvain Paris, and Taesung Park. Scaling gans for text-to-image synthesis. In CVPR, pp. 10124-10134, 2023.
Tero Karras, Miika Aittala, Timo Aila, and Samuli Laine. edm. NeurlPS, 35:26565-265777 2022.
Diederik Kingma, Tim Salimans, Ben Poole, and Jonathan Ho. On density estimation with diffu- sion models. In A. Beygelzimer, Y. Dauphin, Liang, and J. Wortman Vaughan (eds.), NeurlPS. 2021. URL /ttpstsss//ppeeeeiiiiie wtwp://wwwwweeeeeeooouuuummma 2at.ruummmd222LLxxc11122
Yuval Kirstain, Adam Polyak, Uriel Singer, Shahbuland Matiana, Joe Penna, and Omer Levy. Pick- a-pic: An open dataset of user preferences for text-to-image generation. Advances in Neural Information Processing Systems, 36:36652-36660 2023.
Sangyun Lee, Beomsu Kim, and Jong Chul Ye. Minimizing trajectory curvature of ode-based gen- erative models. ICML., pp. 18957-18973. PMLR, 2023.
Sangyun Lee, Zinan Lin, and Giulia Fanti. Improving the training of rectified flows. arXiv preprint 2.Ki:24005.20320 2024.
Shanchuan Lin, Anran Wang, and Xiao Yang. Sdxl-lightning: Progressive adversarial diffusion distillation. arXiv preprint arXiv:2402. 13922, 2024.
Tsung-Yi Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dollár, and C. Lawrence Zitnick. Microsoft COCO: common objects in context. In ECCV, volume 8693, pp. 740-755. Springer, 2014.
Yaron Lipman, Ricky TQ Chen, Heli Ben- Gen-Hamu, Maximilian Nickel, and Matt Lc. Flow matching for generative modeling. arXiv preprint arXiv:2210.0274. 2022.
Xingchao Liu, Chengyue Gong, and Qiang Liu. Flow straight and fast: Learning generate and transfer data with rectified flow. arXiv preprint (2XXXiv:209000000 2022.
Xingchao Liu, Xiwen Zhang, Jianzhu Ma, Jian Peng, et al. Instaflow: One step enough for high-quality diffusion-based text-to-image generation. In ICLR, 2023.
Cheng Lu, Yuhao Zhou, Fan Bao, Jianfei Chen, Chongxuan Li, and Jun Zhu. Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps. NeurlPS, 35:5775-5787, 2022.
Simian Luo, Yiqin Tan, Longbo Huang, Jian Li. and Hang Zhao. Latent consistency models: Syn- thesizing high-resolution images with few-step inference. arXiv preprint arXiv:2310.04377 2023.
Xiaofeng Mao, Zhengkai Jiang, Fu- Yun Wang, Wenbing Zhu, Jiangning Zhang, Hao Chen, Mingmin Chi, and Yabiao Wang. Osv: One step enough for high-quality image to video generation. arXiv preprint 2i0v 1367, 2024.
Chenlin Meng, Robin Rombach, Ruiqi Gao, Diederik Kingma, Stefano Ermon, Jonathan Ho, and Tim Salimans. On distillation of guided diffusion models. In CVPR, pp. 14297-14306, 2023.
Alex Nichol, Prafulla Dhariwal, Aditya Ramesh, Pranav Shyam, Pamela Mishkin, Bob McGrew, Ilya Sutskever, and Mark Chen. Glide: Towards photorealistic image generation and editing with text-guided diffusion models. arXiv preprint arXiv:21 2021.
William Peebles and Saining Xie. Scalable diffusion models with transformers. In ICCV, pp. 4195- 4205, October 2023.
Dustin Podell, Zion English, Kyle Lacey, Andreas Blattmann, Tim Dockhom, Jonas Müller, Joe Penna, and Robin Rombach. Sdxl: Improving latent diffusion models for high-resolution image synthesis. arXiv preprint arXiv:2307.01952, 2023.
13

---

Published as a conference paper at ICLR 2025
Aram-Alexandre Pooladian, Heli Ben- Ham-H Carles Domingo-Enrich, Brandon Amos, Yaron Lip- man, and Ricky TQ Chen. Multisample flow matching: Straightening flows with minibatch cou- plings. arXiv preprint uxXiv2330.114772 2023.
Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, et al. Learning transferable visual models from natural language supervision. In ICLR, pp. 8748 8763. PMLR, 2021.
Aditya Ramesh, Mikhail Pavlov, Gabriel Goh, Scott Gray, Chelsea Voss, Alec Radford, Mark Chen, and Ilya Sutskever. Zero-shot text-to-image generation, 2021. URL httpp::/axxxi..... abs /2102. 12092
Aditya Ramesh, Prafulla Dhariwal, Alex Nichol, Casey Chu, and Mark Chen. Hierarchical text- conditional image generation with clip latents. arXiv preprint arXiv:2204.06125 1(2):3, 2022.
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High- 2022a.
resolution image synthesis with latent diffusion models. In CVPR, pp.
Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Bjöm Ommer. High- resolution image synthesis with latent diffusion models. In CVPR, pp. 10684-10695, 2022b.
Chitwan Saharia, William Chan, Saurabh Saxena, Lala Li, Jay Whang, Emily Denton, Seyed Kam- yar Seyed Ghasemipour, Burcu Karagol Ayan, S. Sara Mahdavi, Rapha Gontijo Lopes, Tim Sal- imans, Jonathan Ho, David J Fleet, and Mohammad Norouzi. Photorealistic text-to-image dif- fusion models with deep language understanding, 2022. URL 2205. 487
org/ /bs/
Tim Salimans and Jonathan Ho. Progressive distillation for fast sampling of diffusion models. arXiv preprint 2XXv:2202.00512. 2022.
Axel Sauer, Tero Karras, Samuli Laine, Andreas Geiger, and Timo Aila. Stylegan-t: Unlocking the power of gans for fast large-scale text-to-image synthesis. In ICML, pp. 30105-301188 PMLR, 2023a.
Axel Sauer, Tero Karras, Samuli Laine, Andreas Geiger, and Timo Aila. Stylegan-t: Unlocking the power of gans for fast large-scale text-to-image synthesis. In ICLR, pp. 30105-30118, PMLR, 2023b.
Axel Sauer, Dominik Lorenz, Andreas Blattmann, and Robin Rombach. Adversarial diffusion dis- tillation. arXiv preprint arXiv:2311.17044 2023c.
Christoph Schuhmann.
Laion-aesthetics.
https:///laion.ai/bl/
laion-assthetics 2022. Accessed: 2023-11-10.
Xiaoyu Shi, Zhaoyang Huang, Fu- Yun Wang, Weikang Bian, Dasong Li, Yi Ziang, Manyuan Zhang, Ka Chun Cheung, Simon See, Hongwei Qin, et al. Motion-i2v: Consistent and controllable image-to-video generation with explicit motion modeling. In SIGGRAPH, pp. 1-11, 2024.
Uriel Singer, Adam Polyak, Thomas Hayes, Xi Yin, Jie An, Songyang Zhang, Qiyuan Hu. Harry Yang, Oron Ashual, Oran Gafni, et al. Make-a-video: Text-to-video generation gentrraatiogggn without text-video data. arXiv preprint arXiv:2209.1477 14792, 2022.
Jiaming Song. Chenlin Meng, and Stefano Ermon. Denoising diffusion implicit models. arXiv preprint arXiv:2010.02502, 2020a.
Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. basee generative modeling through stochastic differential equations. arXiv preprint arXiv:201 13456, 2020b.
Yang Song, Prafulla Dhariwal, Mark Chen, and Ilya Sutskever. Consistency models. arXiv preprint arXiv:2303.01469, 2023.
Alexander Tong, Kilian Fatras, Nikolay Malkin, Guillaume Huguet, Yanlei Zhang, Jarrid Rector- Brooks, Guy Wolf, and Yoshua Bengio. Improving and generalizing flow-based generative models with minibatch optimal transport. arXiv preprint arXiv:2302.00482. 2023.
14

---

Published as a conference paper at ICLR 2025
Bram Wallace, Meihua Dang. Rafael Rafailov, Linqi Zhou, Aaron Lou, Senthil Purushwalkam, Stefano Ermon, Caiming Xiong, Shafiq Joty, and Nikhil Naik. Diffusion model alignment using 2024.
direct preference optimization. In CVPR, pp.
Fu- Yun Wang, Zhengyang Geng, and Hongsheng Li. Stable consistency tuning: Understanding and improving consistency models. arXiv preprint arXiv:2410. 2024a.
Fu- Yun Wang, Zhaoyang Huang, Alexander William Bergman, Dazhong Shen, Peng Gao, Michael Lingelbach, Kegiang Sun, Weikang Bian, Guanglu Song, Yu Liu, et al. Phased consistency model. arXiv preprint arXiv:2405. 2024b.
Fu- Yun Wang, Zhaoyang Huang, Weikang Bian, Xiaoyu Shi, Keqiang Sun, Guanglu Song. Yu Liu, and Hongsheng Li. Animatelem: Computation--effcciett personalized style video generation with- out personalized video data. In SIGGRAPH Asia 2024 Technical Communications, pp. 1-5. 2024c.
Fu- Yun Wang, Zhaoyang Huang, Qiang Ma, Guanglu Song, Xudong Lu, Weikang Bian, Yijin Li, Liu, and Hongsheng Li. Zola: Zero-shot creative long animation generation with short video model. In ECCV, pp. 2299345.20 Springer, 2024d.
Fu-Yun Wang, Zhaoyang Huang, Xiaoyu Shi, Weikang Bian, Guanglu Song, Yu Liu, and Hongsheng Li. Animatelem: Accelerating the animation of personalized diffusion models and adapters with decoupled consistency learning. arXiv preprint arXiv:2402.00769 2024e.
YunYun Wang, Xiaoshi Wu, Zhaoyang Huang, Xiaoyu Shi, Dazhong Shen, Guanglu Song, Liu, and Hongsheng Li. Be-your Mastering video outpainting through input-specific adap- tation. In ECCV, pp. 153-168. Springer, 2024f.
Xiaoshi Wu, Yiming Hao, Keqiang Sun, Yixiong Chen, Feng Zhu, Rui Zhao, and Hongsheng Li. Human preference score v2: A solid benchmark for evaluating human preferences of text-to- image synthesis. arXiv preprint arXiv:2306.09341, 2023.
Jiazheng Xu, Xiao Liu, Yuchen Wu, Yuxuan Tong, Qinkai Li, Ming Ding, Jie Tang, and Yuxiao Dong. Imagereward: Learning and evaluating human preferences for text-to-image generation. Advances in Neural Information Processing Systems, 36, 2024a.
Yanwu Xu, Yang Zhao, Zhisheng Xiao, and Tingbo Hou. Ufogen: You forward once large scale text-to-image generation via diffusion gans. In CVPR, pp. 8196-8206, 2024b.
Yilun Xu, Shangyuan Tong, and Tommi Jaakkola. Stable target field for reduced variance score estimation in diffusion models. arXiv preprint arXiv:2302.00670 2023.
Hanshu Yan, Xingchao Liu, Jiachun Pan, Jun Hao Liew, Qiang Liu, and Jiashi Feng. Perflow: Piecewise rectified flow as universal plug-and-play accelerator. arXiv preprint arXiv:2405.07510, 2024.
Ling Yang, Zixiang Zhang, Zhilong Zhang, Xingchao Liu, Minkai Xu, Wentao Zhang, Chenlin Meng, Stefano Ermon, and Bin Cui. Consistency flow matching: Defining straight flows with velocity consistency. arXiv preprint arXiv:2407.02330 2024.
Tianwei Yin, Michaël Gharbi, Richard Zhang, Eli Shechtman, Fredo Durand, William Freeman, and Taesung Park. One-step diffusion with distribution matching distillation. In CVPR, pp. 6613- 6623, 2024a.
Tianwei Yin, Michaël Gharbi, Taesung Park, Richard Zhang, Eli Shechtman, Fredo Durand, and William T. Freeman. Improved distribution matching distillation for fast image synthesis, 2024b.
URL htthhtts///xxiii org/ absp://bb///400 1100005.116555 14867
Jiahui Yu, Yuanzhong Xu, Jing Yu Koh, Thang Luong, Gunjan Baid, Zirui Wang. Vijay Vasudevan, Alexander Ku, Yinfei Yang, Burcu Karagol Ayan, et al. Scaling autoregressive models for content- rich text-to-image generation. arXiv preprint ar Xiv:2206.10788, 2(3):5, 2022.
15

---

Published as a conference paper at ICLR 2025
Hui Yuan, Kaixuan Huang, Chengzhuo Ni, Minshuo Chen, and Mengdi Wang. Reward-directed conditional diffusion: Provable distribution estimation and reward improvement. Advances in Neural Information Processing Systems, 36:60599-6008 60635, 2023.
Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as perceptual metric. In CVPR, June 2018.
Mingyuan Zhou, Zhendong Wang, Huangjie Zheng, and Hai Huang. Long and short guidance in score identity distillation for one-step text-to-image generation. arXiv preprint arXiv:2406.0156)
2024a.
Mingyuan Zhou, Huangjie Zheng, Zhendong Wang. Mingzhang Yin, and Hai Huang. Score identity distillation: Exponentially fast distillation pretrained diffusion models for one-step generation. In ICML, 2024b.
Yufan Zhou, Ruiyi Zhang, Changyou Chen, Chunyuan Li, Chris Tensmeyer, Tong Yu, Jiuxiang Gu, Jinhui Xu, and Tong Sun. Towards language-fice free training for text-to-image generation. In CVPR, pp. 17907-17917, 2022.
16

---

Published as a conference paper at ICLR 2025
APPENDIX
Related Works
Proof for first-order approximate ODE path
Limitation
IV Why perfect coupling leads to first-order approximate ODE path?
Validation
VI Empirical evidence for the superiority of Rectified Diffusion.
V2 More validation additional datasets.
VI More Discussion
VL
Motivation and contributions
VI.2
Clarification on the difference between rectified diffusion and consistency distillation.
VL.3 Clarification on the additional distillation procedure after rectification.
VI.4 Clarity on the difference between DPM-Solver and Rectified Diffusion
VIlMore results
I RELATED WORKS
Diffusion models. Diffusion models have steadily become the foundational models in image syn-
thesis (Ho et al. 2020, Song et al. 2020b: Karras et al. 2022). Extensive research has been con-
ducted to explore their underlying principles (Lipman et al. 2022 Chen & Lipman 2023 Song
jet al., 2020b Kingma et
2021 Chen al., 2023 2024 Guo et al. 2025 Yuan al. 2023)
and to expand or enhance the design space of these models (Song et al. 2020a Karras et al. 2022
Kingma et al. 2021). Additionally, several works have focused on innovating the model architec-
ture (Dhariwal& & Nichol 2021 Peebles & Xie(2023) while others have scaled diffusion models
for text-conditioned image synthesis and various real-world applications (Shi et al. 2024 Rombach [024e d). Moreover, efforts to accelerate sampling
et al.
2022b Podell et al. 2023 Wang al.
have been pursued at both the scheduler level (Karras et al.; [0222] Lu et al. 2022 Song et al. (2020a)
and the training level (Meng al. 2023 [oon et al. [023] /hou al. 2024h a). The former typi- cally involves refining the approximation of the PF-ODE (Lu et al. [022] Song et al. 2020a), while
the latter focuses on distillation techniques (Meng et 2023 Salimans Ho 2022 Song al.)
2023 Wang et al. 2024b a Mao et al. [2024] Geng et al. 2024) or initializing diffusion weights
for GAN training Sauer el 2023c
Lin al. 2024 Xu al. (0244).
Rectified flow. Lipman et al.
(2022) proposes the flow matching based on continuous normaliz-
ing flows. providing different and unified perspective to understand diffusion models. Liu et al.
(202)) proposes the method rectified flow, setting up important baseline for diffusion acceleration and providing solid theoretical analysis. It proposes rectification to straighten the ODE path of flow-matching based diffusion models. In the proof, [iu et al. (2022) show that the rectification allows for non-decreasing straightness ODE, Liu et al. (2023) scale up the idea of rectified flow into large text-to-image generations, achieving one-step generation without introducing GAN. Yan et al. (2024) and Yang et al. (2024) propose to split the ODE path into multi-phase following the In- staFlow (Liu et 2023). Lee et al. (2024) analysises that one- time rectification is generally enough to achieve pure straightness and proposes better optimization strategy for enhanced performance of rectified flows.

---

Published as a conference paper at ICLR 2025
Stochastic interpolants. Stochastic Interpolants (Albergo al. 2023 Albergo & Vanden -ijnenn-Eijnenn
2022) unifies flow-based and diffusion based methods by extending the framework of continuous- time normalizing flow with continuous-time stochastic processes that bridge arbitrary probability densities in finite time, enabling flexible, noise-adjustable deterministic and stochastic generation while linking score-based diffusion and Schrodinger bridges.
Noise coupling. In addition to rectified flow, which constructs pairwise relationships between data and noise using pretrained diffusion models, there are several other methods that reduce the variance of noise-sample pairings by measuring the distance between noise and samples. For instance, OT- CFM (Tong al. 2023) and Multisample Flow Matching (Pooladian al. 2023) propose building pairing probability matrix by computing the optimal transport relationship between samples and noise within a batch. Similarly, Fast-ODE (Lee al. 2023) suggests training a variational encoder to model data-dependent noise distribution during training. Although these techniques have been validated within the context of flow models, our analysis in this paper suggests that they are broadly applicable to the general framework of diffusion models. Additionally, SFT (Xu et al. 2023) and SCT (Xu et al. 2023) numerically solve the variance-reduced score function of the data distribution, significantly lowering the training variance in both diffusion models and consistency models.
II PROOF FOR FIRST-ORDER APPROXIMATE ODE PATH
Theorem For the general diffusion form X, form as follows:
0x8o + 0,6, there exists an exact ODE solution
Xx
Xa
Ott.
e Ex (2)d
(7)
as
where X = as and ty the inverse function of dr. The first-order approximate ODE path satisfies
Ct x, - (x,00
at / e d>
_
- -x,o 8)
at
show the equivalence between Equation and Equation arbitrary and 8, which holds true and only if eo (x(x is constant.
Proof If (x(,, t) constant, then the Equation 7 and Equation 8 are equivalent.
Assumption: Let (x s) Eo be constant.
Substituting 6n into the Equation
at X, - 01,60 ('m
phe
X₁
-dd
(9)
Calculating the integral:
e -dd = =6 _
0, 0:
(10)
Substituting the result:
0.
X1 0ss
X,
09:00
(11)
O2s
ax
Comparing with the equation: The results match, thus proving equivalence.
If Equation 7 and Equation 8 are equivalent, then (x(x); must be constant. Assumption: Assume the two are equivalent:
de -0t e ex lx)dA -mEe((8s:)) J de
(12)
2

---

Published as a conference paper at ICLR 2025
Removing the constant factor:
Ad
Ex( tx)dA co(x.. Lmm e *d
(13)
Differentiating with respect to with Newton- Leibniz theorem:
dt (1
d 200xxxx
Ae
dd N
(14)
dt
Comparing both sides:
dd
dhe dl
E A -xxEe(xxx (xxxxxX,)) (2)
60(xx S)e
(15)
di
As indicated by previous work Kingma et al. function. Therefore, we have d In ae
2021 J SNR(t) = o/ is the monotonically decreasing
(IS(((()) is a monotonically decreasing function. 0, cancel terms. leading to:
0e
Therefore ddc < O. Since dd, + 0 and de
co(x,, (x) cx s), Vtx [s,
(16)
This shows that for any I, cx(x,, must be constant, proving the "if and only if" statement.
III LIMITATION
At low-step regime, the performance of methods based on rectification still lags behind state-of- the-art methods based on distillation (Zhou et al. 2024b) or GAN training (Yin et al. 2024b Sauer ctt al. 2023c). Additional distillation steps are needed to improve low-step performance, which is also stated in InstaFlow (Liu et al. 2023).
IV WHY PERFECT COUPLING LEADS TO FIRST-ORDER APPROXIMATE ODE PATH?
For diffusion model trained with the form X; agXo + diE (Kingma et al. 2021). The score se will converge to the expectation value of all the possible conditional scores V log I ((r which is determined by data Xu and noise (Vx, log (xx,
-x due to the noise and data of
Xo is randomly paired (Song et al. 2020b). That
so sx f) = Ep(xa xx) Xx, log (x))].
(17)
The expectation score value on the same PF-ODE but different timesteps will converge different values and directions (Song et al.) 2020b Therefore, on the PF-ODE, the score sø(x,, t) will change along the time axis. Since along the time axis, which is not comprised with our theorem 1. It is not first-order approximate ODE path.
0,80 means that the epsilon prediction will change
However, if we achieve perfect noise data coupling and satisfy the no-intersection condition, x, will be sampled with a single noise and data pair. Without optimization errors, we will have
X,
ax
se (x t) Xx, log Pxx;
xx)
(18)
of
Since Eg = -0,Sp therefore the epsilon prediction on the PF-ODE should always be the e. Return our Theorem [] that is say, we achieve the first-order approximate ODE path.

---

Published as a conference paper at ICLR 2025
V VALIDATION
V.I EMPIRICAL EVIDENCE FOR THE SUPERIORITY RECTIRIED DIFFUSION.
Rectified Diffusion outperforms Rectified Flow with significantly smaller training costs. As highlighted in Fig. 2 where we show the performance change as the training iterations. Our one-step performance signihcantly outperforms the one-step performance of the official weight of Rectified Flow (Liu et al. 2023) within only 20, 000 iterations with batch size 128. The overall number of trained images at this iteration only 8% of the number of trained images in Rectified Flow. Even after the full training of 200, 000 iterations, considering that our batch size adopted is only 128 which is significantly smaller than the batch size adopted in previous work, we still use less trained images than the official weight of Rectified Flow method.
Rectified Diffusion significantly outperforms Rectified Flow in the few-step setting, The perfor- mance in the stw-step setting is the most important criterion to judge the effectiveness of rectification on the ODE (since we aim to achieve efficient sampling and improve the performance in few-step sampling). Rectified Diffusion significantly outperforms Rectified Flow in this setting. Specifically, on COCO-5K. Rectified Flow achieves one-step FID 47.91, and two-step FID 31.35. Instead, Recti- fied Diffusion achieves one-step FID 27.26 (significantly outperforms the two-step FID of Rectified Flow), and two-step FID 22.98 (approaching the 25-step FID of Rectified Flow 21.65). The is strong evidence that Rectified Diffusion is better than Rectified Flow.
Rectified Diffusion has better performance upper bound than Rectified Flow. It should be noted that Rectified Diffusion and Rectified Flow are all trained with generated data from pretrained diffusion models. Specifically, in the default setting, they both use 25-step DPMSolver with Stable Diffusion v1-5 to generate noise-data pairs. Therefore, the performance of 25-step DPMSolver with the teacher diffusion model works as the performance upper-bound. The 25-step Rectified Diffusion achieves better performance than 25-step Rectified Flow on both FID and CLIP SCORE. Therefore, Rectified Diffusion has better performance upper bound than Rectified Flow. Additionally, please note that the 25-step performance of Rectified Diffusion and that of Rectified Flow are already very close to the 25-step DPMSolver with the teacher diffusion model. Therefore, we not achieve very large improvement.
Rectified Diffusion (Phased) consistently surpasses the baseline PeRFlow Yaan et al., 2024). We extend Rectified Diffusion into the phased setting, and our performance still consistently outper- forms the previous phased rectified flow-based method.
Rectified Diffusion (CD) surpasses the baseline Rectified Flow (Distill) with only 3% GPU days for training. The distillation process described in the InstaFlow (Liu al. 2023) takes 110 A100 GPU days. Our training cost is approximately 3% of the GPU days of InstaFlow distillation process. Moreover, the results generated by Rectified Flow (Distill) remain relatively blurry and lack the ability for multi-step refinement, which limits its applicability. Instead, Rectified Diffusion (CD) not only achieves better one-step performance but also supports multistep refinement further improve the performance.
V.2 MORE VALIDATION ON ADDITIONAL. DATASETS.
We additionally evaluate model performance on the Laion (Schuhmann) 2022) and CC3M (Chang- pinyo et al. (02T] subsets. Following the test setting of COCO-2017, we adopt the 5k subset for evaluation. Our experimental results shown in Table[[show show that Rectified Diffusion consistently outperforms Rectified Flow, consistent with our original evaluation on the COCO dataset. This provides strong evidence of the superiority of Rectified Diffusion.
VI MORE DISCUSSION
VI.1 MOTIVATION AND CONTRIBUTIONS
The motivation for rectified diffusion is to investigate and rethink the most essential part of rectified flow (Liu et al. 2022). The investigation allows to extend the scope of rectification, which was
4

---

Published as a conference paper at ICLR 2025
Table Performance comparison Laion and CC3M subsets.
Subset
Step
Metric
Rectified Diffusion
Rectified Flow
Laion
8
CLIP Score
26.36
25.49
FID
23.52
24.73
4
CLIP Score
25.80
24.65
FID
24.70
27.27
2
CLIP Score
25.15
23.38
FID
26.14
35.09
CLIP Score
23.30
20.12
FID
30.14
$2.86
CC3M
8
Soore
28.33
27.65
FID
28.10
29.07
4
CLIP Score
28.08
27.37
FID
29.97
31.54
2
CLIP Score
27.68
26.27
FID
31.56
37.72
CLIP Score
26.30
24.63
FID
34.28
49.06
originally proposed and believed only suitable for rectified flow (using the form x; (1- (1-t)xg + te to general diffusion models.
In particular, InstaFlow (Liu al. 2023 an important follow-up work to rectified flow that extends it to text-to-image tasks and serves key baseline in our paper, uses the Stable Diffusion (Which an e-prediction neural network follows DDPM diffusion form) for initialization. However, in InstaFlow, the model is first converted into u-prediction flow-matching model before undergoing retraining paired noise-sample This process introduces a gap between the pretrained model and the retrained model supporting efficient sampling.
The conversion that converts the pretrained diffusion models (can be forms of DDPM, Sub- VP. VE (Song et al. 2020b)) has become common practice in the important following works (Liu et al. 2022 Yan et al. 2024 Lee et al. 2024).
To knowledge, are the first to point out that this conversion is unimportant and show that straightness is not the essential training target. Any ODE (even curved) can achieve one- step sampling long as it satisfies the requirement of first-order approximate property.
Therefore, our main contribution is to rethink and break the incomplete understanding from previ- research. Additionally, make our method simple, straightforward, and accessible pos- sible to most diffusion-related researchers. Essentially, rectified diffusion does not need to change anything of pretrained diffusion models for sampling acceleration (including networks, preconds, training/inference code, noise scheduler, etc.). The only difference as highlighted in our paper is replace the noise and data in standard diffusion training with paired noise (collected) and data (generated).
With this simple design, we still achieve significant improvement compared the previous best- performing rectified flow-based methods (with even smaller training costs) and comparable perfor- mance previous persorerfnnnng distillation or GAN-based acceleration methods. We believe this discovery can inspire related research and broaden the understanding of diffusion models in the community.
VI.2 CLARIFICATION ON THE DIFFERENCE BETWREN RECTIFIRD DIFFUSION AND CONSISTENCY DISTILLATION.
The crucial difference between rectification (aims to achieve first-order approximate ODE path) and distillation (aims to directly predict the solution point of PF-ODE is that rectification will change the ODE trajectory but distillation does not. We provided visualization explanation in Fig. Since it's hard to intuitively determine whether a curved ODE path satisfies first-order property. represent the first-order approximate ODE path with straight line (It is not straight in most cases). Consistency models change the prediction of original diffusion models but do not change the ODE trajectory. This makes only suitable for stochastic multistep sampling (If uses diffusion
5

---

Published as a conference paper at ICLR 2025
samplers like DDIM (Song al. 2020a), it will fall out from the ODE trajectory, causing the further prediction to be degraded). Instead, rectification smoothens and rectifies the ODE trajectory to make it the first-order approximate ODE path. Generally, after rectification, the diffusion model still diffusion model (since its prediction direction still follows the derivative of its ODE as shown in Fig. 5). but performs much better in the few-step setting. Instead, diffusion models after consistency distillation will become consistency models, since its prediction direction is different from the derivative of its PF-ODE.
VI.3 CLARIFICATION ON THE ADDITIONAL DISTILLATION PROCEDURE AFTER RECTIFICATION.
To set up a fair comparison. The most direct reason why we adopted distillation to further improve performance is to set up fair comparison with InstaFlow (Liu et al. 2023). The difference is that we adopt consistency distillation instead of the naive distillation strategy adopted InstaFlow. We achieve better 1-step performance than the distilled baseline in InstaFlow with only 3% GPU days used by InstaFlow for distillation.
Rectification is harder objective than distillation. The root reason that first-order approximate ODE path a harder target than distillation. Intuitively speaking, since the first-order approximate ODE path is stronger constraint than self-consistency, it harder train and will face more optimization issues. However, despite the difficulty of achieving perfect first-order approximate ODE paths, after rectification, the ODE of our model will become generally closer to the first-order approximate ODE path. It will reduce the difficulty of further distillation if we use the model that has undergone rectification as the teacher model for distillation.
VI.4 CLARITY ON THE DIFFERENCE BETWEEN DPM-SOLVER AND RECTIFIED DIFFUSION
Following the proof of DPM-Solver-1 (Equation 3.6 and the subsequent equation Page of DPM- Solver), which is equivalent to the DDIM sampler, we can approximate the ODE solution from time I follows:
X2 (x((x) frr - + A1)3).
(19)
at
In DPM-Selver-L, higher-order error terms O((A, 2x)3) are neglected during inference, which becomes problematic when X X, is large. This is the primary reason why DPM-Solver-1 (DDIM) requires at least 50 steps for high-quality generation.
In contrast, our paper does not rely such level approximations. Our primary goal is to tify the PF-ODE to ensure it satisfies first-order accuracy, which eliminates the high-order er- terms through paired retraining (Rectification). This the fundamental reason why Rectified Diffusion can achieve 1-step generation. In comparison, DPM-Solver requires at least several steps typically over ten-for high-quality generation.
VII
MORE RESULTS

---

Published as a conference paper at ICLR 2025
Table 3: Performance comparison on COCO-2014.
Method
Res.
Time (J)
Steps
# Param.
FID (
CLIP
Autoregressive Models
DALL-E Rameah et al. 2021
256
12B
27.5
CogView Ding at
6B
24.0
Parti-750M
256
750M
10.71
Parti-B (Yu et 20264
256
6.4s
3B
8.10
Purti-20B a. 2022
20B
7.23
Make-A-Stan
2022
256
25.0s
11.84
Masked Models
Muse (Chang et al. 2023
1.3
3B
7.88
0.32
Diffusion Models
GLIDE Nichol 202
256
15.0s
5B
12.24
DALL 52 Kamesh
2124
256
250+27
5.5B
10.39
LDM (Ronbach et
20229
3.7s
250
1,45B
12.63
Imagel Salaana
256
9.1s
3B
7.27
eDiff-I
Baljji et al
256
32.0s
25+10
9B
6.95
Generative Adversarial Networks (GANs)
LAFITE Zhou et al. 2022
256
0.02s
75M
26.94
StyleGA N Sauer
0.10s
18
00.293
GigaGAN K Lig 2045
512
0.13s
IB
9.09
Stable Diffusion (0.9 B) and its accelerated distilled versions
GANs
UFOGen Xu
2024b
0.09s
0.9B
12.78
DMD (CHG3) Yin
2024a
512
0.19%
0.98
11.49
DMD (CFG=8) Yun et 2024a
512
0.09s
0.9B
14.98
0.320
SD-Turbo (Sauer al. 20236
0.09s
0.9B
16.59
0,312
Distillation
BOOT (Gu 2023
512
0.09s
0.9B
48,20
0.26
Guided Distilation MMan et al. 2023
0.09s
0.9B
37.3
0.27
LCM (Luo al. 2025
512
0.09s
0.9B
37.3
0.27
Phased Consistency Model Wang et al.
2024b
512
0.09%
0.98
17.91
0.296
Phased Consistency Model Wang ct al.
2024b
0.21s
0.9B
11.70
SID-LSG 4.5)
512
0.09s
0.9B
16.59
0.317
SID-L (x = 3)
512
0.09%
0.98
13.21
0,314
SID-LSG (x 2)
0.09s
0.9B
9.56
0,313
SID-LSG 1.5)
0.09s
0.9B
0,302
SG (N: 4.5)
512
0.19%
0.98
16.59
0.317
Rectification (+
SDvL-S+DPMSolver (Upper-Bound) Lu
2022
512
0.88s
0.9B
9.78
0.318
Rectified Flow (Liu
2023
512
0.88s
0.9B
11.34
0.313
Rectified Flow Liu ct
2023
512
0.09s
0.9B
36.68
0.272
Rectified Flow Liu et al
A023
512
0.13s
0.9B
20.01
0.296
Rectified
(Ours)
0.88s
0.315
Rectified Diffusion (Ours)
512
0.09s
0.9B
16.88
0.293
Rectified Diffusion (Ours)
512
0.13s
0.9B
12.57
0,307
Rectified Flow (Distill) Liu al 2023
512
0.09s
0.9B
13.67
0.302
Rectified Flow (Distill) Luu et 2023
0.13s
0.9B
0.261
Rectified Diffusion (CD) (Ours)
512
0.09x
0.98
12.54
0.303
Rectified Diffusion (CD (Our)
512
0.13s
0.9B
11.41
0.310
PeRFlow Yan ct al. 2024
512
0.21s
0.9B
18.59
0.264
Rectified Dillusion (Phase (Ours)
0.21s
0.9B
10.21
Stable Diffusion XL (3B) and its accelerated or distilled versions
GANs
SDXL. Turbo Sauer et al.
2023e
512
0.15s
3B
24.57
0.337
SDXL-Turbo Sauer 2t at
2025c
0.34s
3B
23.19
0.334
SDXL-Lighting
1024
0.35s
3B
23,92
0.316
SDXI Lightning In 21
2124
1024
0.71s
4
3B
24.56
0.323
DMDv2
Yin al. 202415
1024
0.35s
3B
19,01
0.336
DMDv2
1024
0.71s
3B
19.32
0.332
Distillation
LCM (Luo al. 2023
1024
0.35s
3B
81.62
0.275
LCM
1024
0.71s
3B
22.16
0.317
Phased Consislency Model
Wang et al. 2024h
1024
0.35s
3B
25.31
0,318
Phased Consistency Model
Wang et at. 20246
1024
0.71s
3B
21.04
0.329
Rectification (*
PeRFlowXLL Yun et 2024
1024
0.71s
4
3B
20,99
0.334
Rectified Difhisson XI. (Phased) (Ours)
1024
0.71s
3B
19.71
0.340
Results Stable Diffusion XL-based models
COCO-2014 following evaluation setting DMDv2
2024b
Other resalts are tested with COCO-2014 30k following the karpathy split.

---

Published as a conference paper at ICLR 2025
Rect Reet How
Doctified Diflusion flceiffe Diffusioo
1-stap
I-step
Prompee yanding lis hark, Sk Phomppss Image A goot weshing thick wooezzl oiilee cat cal aodd acaii ciausing co top theaey mo datn palk, good sllvenin to Interodl that aee chattriing louily, aausi of thy icides
Reciheed flow
2.5000
Bectifid Diffusion
Rechited How
4.301p
Beciifee billosan 8
Rectriee Now stopp
Bactifiel Diflision
Recthhed slow 15 stip
15 25-p
Reciifieed DiF snion (it (CD)lteciifed Diffovin (CD) nectifidd Difiasion
Rectified Flow 25 25-eup
25-cuup
meceited slow (Dcal) neceited How (Doad) stepp
1.000p
aouuiifl owmann purteed by Goggh night"
bend and to the gi gond cratting mosking sound to they shatter.
Deciiiiee Difluvan (Paased) step
Pe low <.ttpp
Ructhaed Difutioon SOOL (Phssed)
Rettiow SOIL
4.20p
Pronpt
Figure 8: Qualitative comparison.
8

---

Published as a conference paper at ICLR 2025
Rest-hed How
fleetffed Diffusiio
1-00p
1-00p
Deciified Diflusion
Recifeed Flow 2.30pp
2000
Bectffed Diffusion
Rechited How
4.301p
Beciifeed billovan
Recereed Flow
8-ste0 st0p
8
Bactified Diflaiion
Reathhed Flow 15 20pp
15 S0pp
Rectifiee Di snion o (ccfftcciiiie Diffuvio (CD) neciileed Diftasion
Rectiied Flow 25-00p
25.0up
neceited How (Doa4)
1.000
Prompt-2 C06 CI Cortiial Damooi Solttaee frala King" PropltS The Row Rber Roer by BoodliConnt
Receited flow (Deell
-tepp
Deciified Difluvan (Phssed) (Paased) step
Fuller VE
Pe Oo <.0app
Ructtred Dimttonn
Pumple "1933
Pettiow SORL
4.2up
Figure 9: Qualitative comparison.
9

---

Published as a conference paper at ICLR 2025
Prompt 'slll life photo of apple."
Proript: "A walking the moon."
Promptt: "guinea Pigs on pirate ship.
Prompt lusky running on the beach."
Promptt 'insandly detailed portrait lercale model, imsane face perfect soes. dolr extremely intricate, 8k....
Prompt: "Photoreslitic Hlonde gid in pyjama"
Prompt: "best merkers 14569 aboch NIKED Lebion Soldier 12 Resigns I Sele Collerbor."
Phomit:: REPUBLIC Relaved Straihht Log jetns.
Main, color, 490
Prompti Vava
Faux Curlsin."
Prompt: "Chuck Taylor Star Hi VN."
PeRFlow-XL
Rectified Diffusion-XL
PeRFlow-XL
Rectified Diffusion-XL
Figure 10: Qualitative comparison.
10


Reviews:
[{"review_id": "BT7NbWZlo1", "reviewer": "Reviewer_sELj", "summary": "This paper proposes Rectified Diffusion that generalizes rectified flow to broader categories of diffusion models, improving image generation efficiency by removing the need for flow-matching and v-prediction. Key components of the proposed method include pre-computed noise-sample pairs, consistency distillation, and phased ODE segmentation, allowing the model to achieve comparable or superior quality with fewer training steps.", "questions": "1. The performance metrics on FID shows only marginal improvements over Rectified Flow. The FID metric for Rectified Flow shown in Table 2 corresponding to step2 (62.81) is higher than step1 (13.67). Are these values correct? Generally step2 value should be lower.\n2. Could the authors validated the performance of their method on more datasets?", "limitations": "", "rating": 8, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The authors  generalized rectified flow to a wider array of diffusion models by focusing on paired noise-sample training, making the approach compatible with different prediction types and diffusion models.\n2. The paper demonstrates that Rectified Diffusion performs better than prior methods like InstaFlow and Rectified Flow in terms of FID and CLIP scores, particularly when generating images in low-step regimes.\n3. By dividing the ODE path into phases with enforced linearity in each phase, the model maintains a balance between quality and computational efficiency without altering the fundamental diffusion trajectory.", "weaknesses": "1.  While the approach seems efficient, the paper builds on existing methods, particularly using paired noise-sample training, phased ODE segmentation and consistency distillation. The lack of entirely new techniques could limit its novelty in diffusion model research.\n2. While this method employs distillation techniques that improve inference speed, achieving single-step image generation without pre-trained models could introduce a novel advancement.\n3. The performance metrics on FID shows only marginal improvements over Rectified Flow. The FID metric for Rectified Flow shown in Table 2 corresponding to step2 (62.81) is higher than step1 (13.67). Are these values correct? Generally step2 value should be lower.\n4. Although the method is compared against multiple models, all experiments are limited to a single dataset (COCO). Additional experiments on other benchmark datasets, such as ImageNet, would help validate the generalizability of the results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "plolcGiaFE", "reviewer": "Reviewer_KrPe", "summary": "This paper presents two findings, one is that straightness as required in rectified flow is not necessary, and second is that it proposed Rectified Diffusion, which generalizes the design space and application scope of rectification to diffusion models.", "questions": "From eq 13 to eq 14, it asserts that d\\lambda_t/dt is not zero, what is that? Or as \\lambda_t = ln \\alpha_t / \\sigma_t, is it always true that this partial derivative is non-zero? \nTable 1, second block, it seems for example Rectified Flow's FID had great improvement from 1 step to 2 steps then to 25 steps, the Rectified Diffusion's FID did not show a great improvement from 1 step to 2 steps then to 25 steps, while the Rectified Diffusion's FID at 25 steps is slightly better than the FID of Rectified Flow at 25 steps. Can authors elaborate on why Rectified Diffusion does not experience a much-improved performance from 1 step to 25 steps? \nFigure 2 is somehow difficult to understand. Why did the FID and CLIP score of Rectified Flow not change with iterations?\nFigure 6, the two rightmost plots, why did the curves of Rectified Diffusion go up at 4 and 8 steps? Does it mean the method need to stop at some optimal points before its performance decreases? And if so, how does one determine the proper steps to stop? \nIn Figure 7, it seems the biggest difference in preference given by human evaluation is the Phased 4-step results. Does it imply that Phased implementation, which features multiple straight trajectories rather than one single straight trajectory generally, generally gives better results? Also, in Phased implementation, how many phases were used? It seems this information is not given in the paper.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "First strength is that the paper shows that straightness is necessary as required in rectified flow. It shows that rectified flow is a special case of rectified diffusion, which is what the paper proposed as a better generative model. \nSecond strength is the better quantitative results and favorable comparison with other methods.", "weaknesses": "Maybe I am missing something, it seems the paper argues that straightness of the ODE trajectory is not necessary, but its results appear to show a straight path, such as Figure 4 and Figure 5. \nOther weaknesses include that from visual evaluation, it seems that though the rectified diffusion gave better images than rectified flow in most cases, the improvement is not always clear. For example, in Figure 10, the result of rectified diffusion on the sneakers seem that the string missed a buttonhole. Also, in the pajama example, figure patterns on the pajama in the rectified diffusion result are not as sharp as those on the result of rectified flow. In Figure 10, the huskie images generated by both ReFlow and Rec Diffusion seem to have an extra leg, though it is more evident in the image generated by ReFlow.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "siWPLgrf86", "reviewer": "Reviewer_t4qC", "summary": "This paper proposed to study the essence of rectified flow and proposed Rectified Diffusion.", "questions": "1. Please correct the typo \"obeserve\" in Page 5 line 265 and if there is any more.\n 2. In Page 5 around line 265, the authors stated that the trajectory of y_t is a straight line from the initial point ϵ towards the direction of x0 (as shown in Figure 3 (e). This is not clearly explained. Also, It seems like a very special case  when they only used X0 = [0, 1]. It would make more sense if the authors generate the trajectories over time for each elements of X_0 to \\epsilon.\n3. In Page 4, line 205, the authors mentioned that there exists an exact ODE solution form from Lu et al., 2022, but they omitted the solution was  for  what first order ODE. That will easily confuse the readers.\n4. Eqn (2)  in Page 4 should be just an linear approximation of curves. You can use a straight line to approximate the curve, but then you can say this linear line is the result of a straight flow ode.\n5. Some descriptions seem like claims that need to be further elaborated, for example those in line 250-line 261.", "limitations": "", "rating": 1, "confidence": 4, "soundness": 1, "presentation": 2, "contribution": 1, "strengths": "They tried to highlight that straightness is not an essential training target for rectification.", "weaknesses": "It was not stated clearly why it is necessary to study whether straightness is not an essential training target for rectification. To me, it was the straightness used in the ode of the rectified flow algorithm that causes the usage of rectified flow, thus it seems trivial that there is no need to use the rectified flow in a ode that does not follow a straight line. \n\nThe diffusion that follows the curve form that the authors proposed is mentioned in some papers including the original rectified flow paper with the formula listed as well. It can return back to DDPM or DDIM; therefore, to me, it seems like recirculating the algorithm.  The authors might want to look into the following references mentioned in the original rectified flow paper in Lu et al., 2022 (Lipman et al., 2022; Albergo & Vanden-Eijnden, 2022; Heitz et al., 2023).Neklyudov et al. (2022).\nWhile the authors meant to straighten the paths that originally were curves, they can be viewed as approximately meanwhile they can also be viewed as the original straight flows.\nAlthough one can choose any ode path, the paper did not prove (or it is not clear) that their choice gains advantage over existing algorithms. As a matter of fact, the authors used 200000 runs to train the algorithm as shown in figure 2. \n\nAlso, Theorem 1 proved in Appendix seems like a similar version of one in (Lu et al., 2022), there is no need to repeat.\n\nAs a result of the weaknesses stated here, the title of this paper seems like questionable itself ( seems like a logic flaw?).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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": "eduUNsc8NR", "reviewer": "Reviewer_2rVP", "summary": "This paper proposes rectified diffusion, a generalization of rectified flow to first-order ODEs. During training, rectified diffusion aims to correct the learned ODE of the pretrained diffusion model to be closer to a first-order ODE, using precomputed noise-data pairs. Thus the authors argue that using paired noise-data examples is the essential component of both rectified flow and rectified diffusion. The authors further propose phased rectified diffusion and consistency distillation on top of rectified diffusion. In their experiments, they demonstrate superior quantitative and qualitative performance over rectified flow and a previous phased ODE segmentation method (PeRFlow).", "questions": "* In lines 357-358, the authors claim that the first-order ODE objective is a stronger constraint than self-consistency. If it’s the case that first-order ODE => self-consistency, then why would consistency distillation be necessary after rectified flow?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "* The quantitative and qualitative results (Figs. 8-10) are quite convincing. The authors provide the essential baselines of rectified flow and PeRFlow, as well as additional Stable Diffusion XL-based baselines in Table 2.\n* The idea is original yet simple (a strength not a weakness). It is well-backed by a brief theoretical discussion in Section 2.2.\n* Besides a few grammatical errors and too-short figure captions, the presentation is good. The text is easy to follow, and the figures are intuitive.", "weaknesses": "* It would have been nice to compare to Consistency Models (Song et al. 2023) for one-step generation.\n* In Table 1, is there a typo for 25-step Rectified Diffusion (Ours)? It says the time is only 0.09s, which is the same as 1-step Rectified Diffusion (Ours).\n\nNitpick:\n* Figure 4 should have axis labels. \n* Fonts too small to read in Figure 7.\n* Figure 6 caption too short and could use more description.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "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:

Decision: Accept (Poster)