SemFlow: Binding Semantic Segmentation and Image Synthesis via Rectified Flow
Authors: Chaoyang Wang
Xiangtai Li
Lu Qi
Henghui Ding
Yunhai Tong
Ming-Hsuan Yang
Venue: NeurIPS 2024 poster (2024)
Keywords: Segmentation
Diffusion Model
Primary area: diffusion_based_models

Abstract: Semantic segmentation and semantic image synthesis are two representative tasks in visual perception and generation. While existing methods consider them as two distinct tasks, we propose a unified framework (SemFlow) and model them as a pair of reverse problems. Specifically, motivated by rectified flow theory, we train an ordinary differential equation (ODE) model to transport between the distributions of real images and semantic masks. As the training object is symmetric, samples belonging to the two distributions, images and semantic masks, can be effortlessly transferred reversibly. For semantic segmentation, our approach solves the contradiction between the randomness of diffusion outputs and the uniqueness of segmentation results. For image synthesis, we propose a finite perturbation approach to enhance the diversity of generated results without changing the semantic categories. Experiments show that our SemFlow achieves competitive results on semantic segmentation and semantic image synthesis tasks. We hope this simple framework will motivate people to rethink the unification of low-level and high-level vision.

SemFlow: Binding Semantic Segmentation and Image Synthesis via Rectified Flow
Chaoyang Wang' Xiangtai Li!
Lu Qi Henghui Ding
Yunhai Tong* Ming- Ming-Hsuan Yang"
School of Intelligence Science and Technology. Peking University
UC, Merced Institute of Big Data, Fudan University
Project page: https: / //wgg//w/ggaa/aa//e chaoyang. github... wo/project/seeeeeeoeeeeeeeeeesse srroject/semflox semflow cywang stu..pu. www.u.pku.euu.c... edu.cn, qqlu gmail.com, xiangtai94 Mangtai94@gmmii..com gmail.com
Abstract
Semantic segmentation and semantic image synthesis are two representative tasks in visual perception and generation. While existing methods consider them as two distinct tasks, we propose unified framework (SemFlow) and model them pair of reverse problems. Specifically, motivated by rectified flow theory, we train an ordinary differential equation (ODE) model to transport between the distri- butions of real images and semantic masks. As the training object is symmetric, samples belonging to the two distributions, images and semantic masks, can be effortlessly transferred reversibly. For semantic segmentation, the contradiction between the randomness of diffusion outputs and the uniqueness of segmentation results. For image synthesis, we propose finite perturbation approach to enhance the diversity of generated results without changing the se- mantic categories. Experiments show that our SemFlow achieves competitive results on semantic segmentation and semantic image synthesis tasks. We hope this simple framework will motivate people to rethink the unification of low-level and high-level vision.
approach solves
Introduction
Understanding semantic content and creating images from semantic conditions are fundamental
research topics in computer vision. Semantic segmentation [45: 7; 59; 85; 11; 10] and image synthesis [8; 32; 28; 72; 90] are two representative dense prediction tasks and inspires various downstream applications, including autonomous driving [5] and medical image analysis [89]. The former aims to assign category label to each pixel in the image, while the latter aims to generate realistic images given semantic layouts.
Although semantic segmentation and image synthesis constitute a pair of reverse problems, existing works typically solve them using two distinct methodologies. On the one hand, segmentation models mostly follow the spirit of discriminative models. Specifically, a pre-trained backbone is employed to extract multi-scale features, and then sask-spe decoders are used for dense prediction. On the other hand, semantic image synthesis frameworks are mainly built upon generative adversarial networks (GAN) [19; 52; 57; 62] or diffusion models (DM) [63; 64; 25J. GAN-based methods [90; 72: 28] typically take semantic layouts as inputs and adopt discriminator for adversarial training. Meanwhile, DM-based methods [36] generate from noise with semantic layouts functioning as control signals.
An intuitive solution is to represent the segmentation mask as colormap and model it as conditional image generation task [56]. However, there are several implementation challenges. Overall, most of
Corresponding author: Lu Qi and Xiangtai Li.
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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Forward Flow ODE (Semantic Segmentation) dæ; væzz t)dlt
Zo
2
20
dzp -2 t)dt
21 +
Reverse Flow ODE (Semantic Image Synthesis)
Figure 1: Rectified flow bridges semantic segmentation (SS) and semantic image synthesis (SIS). SS and SIS are modeled as a pair of transportation problems between the distributions of images and masks. They share the same ODE and only differ the direction of the velocity field. We propose a finite perturbation operation on the mask to enable multi-modal generation without changing the semantic labels. Grey dots represent data samples. Colored dots represent semantic centroids, also known as anchors in Eq. 7. Colored bubbles represent the scale of perturbation.
the discriminative segmentation models do not apply this problem due to their irreversibility. For generative adversarial networks, their generators are typically unidirectional. Jointly training multiple unidirectional models to achieve bidirectional generation [90] is not the concern of this paper. Latent diffusion models (LDMs) have recently demonstrated great potential in generative tasks. Beyond generative tasks, several works [56; 69] attempt apply diffusion models for segmentation, with images functioning as conditions, but their applicable tasks are limited to be class-agnostic. There three main problems for existing LDM-based segmentation frameworks: 1) The contradiction between the randomness of generation outputs and the certainty of segmentation labels. 2) The huge cost brought by multiple inference steps. 3) The irreversibility between semantic masks and images.
In this paper, we use rectified flow [40; 42; 17] to enable LDM as a unified framework for semantic segmentation and semantic image synthesis. Our key idea is summarized in Fig. 1. Starting from an LDM [58] framework, we solve the above problems with three methodologies. First, we redefine the mapping function address the randomness. Previous works [56] aim to learn the mapping from the joint distribution of Gaussian noise and images to the segmentation masks. We argue that Gaussian noise in this mapping function redundant and negatively affects the determinism of semantic segmentation results. Instead, our model directly learns the mapping from images to masks. Secondly, we make the mapping reversible via rectified flow. Rectified flow an ordinary differential equation (ODE) framework with time-symmetrie training object. This feature allows the model to be trained once to obtain bi-directional transmission capabilities and can be solved numerically using simple ODE solvers such as Euler. Finally, we propose a finite perturbation method enable multi-mon modal image synthesis, the mapping is one-to-one in semantic segmentation but one-to-ne mo-many in semantic synthesis. We add papllttudelliiitee noise, enabling masks to be sampled distributions rather than a fixed value, and further improving
from a collection of the quality of synthesized results. Moreover, our model needs fewer inference steps than traditional diffusion models because the transport trajectory is straight, significantly reducing the gap between LDM and traditional discriminative models in segmentation.
The main contributions semantic segmentation and image synthesis with rectified flow, effectively leveraging the length of the generative models. We propose specialized designs of SemFlow, including pseudo mask modeling, bi-directional training of segmentation and generation. and a finite perturbation strategy. 3) We validate SemFlow on several popular benchmarks. For semantic segmentation, SemFlow dramatically narrows the gap between diffusion models and discriminative models in terms of accuracy and inference speed with more elegant framework. Meanwhile, SemFlow also performs decently in semantic image synthesis tasks.
follows: 1) We introduce SemFlow, new unified framework that binds
Related Work
Diffusion Models and Rectified Flow. Diffusion models [25; 63; 64] have shown impressive results in the field of generation, such image generation [58; 55; 83; 27; 13; 54], video generation [80].

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image editing [4; 46; 60; 51; 231, image super resolution [61; 26] and point cloud [47; 50; 88; 82; 48]. Most of these methods are based on stochastic differential equations (SDEs) and need multiple steps for generation. Recently, some works [40; 39; 38; 1; 22] propose to model with probabilityy flow ordinary differential equations (ODEs) to reduce the inference steps. Specifically, rectified flow [40; 42] defines the forward process as straight paths and uses reflow to mínimize the sampling steps to one. Although rectified flow has demonstrated decent results on image generation and image transfer tasks, they are limited to low-level vision and lack exploration of the unification of segmentation and generation tasks.
Semantic Segmentation is one of the core tasks in visual perception, aiming to assign each pixel of the given image semantic category. Previous semantic segmentation approaches are typically built upon discriminative modeling, consisting of strong backbone [21; 16; 43; 44; 33] for feature extraction and a task task-specin specific decoder head [7: 59; 85: 11; 10; 87; 65; 81; 15; 14] for mask prediction. Recently, some works [34; 86; 18; 77; 75; 3; 70; 9: 20; 2; 29; 76; 71] exploit diffusion models for segmentation. They typically follow the spirit of discriminative models and employ the diffusion model as feature extractor. Although UniGS [56] and LDMSeg [69] attempt use plain Stable Diffusion framework for segmentation, their applicable tasks are limited to be class-agnostic. In practice, reconciling the stochastic outputs of diffusion models with the deterministic results of semantic segmentation is difficult. We rethink this problem and re-model it with rectified flow.
Semantic Image Synthesis is the reverse problem of semantic segmentation, aiming to generate realistic images given semantic layouts [8; 53; 41; 74; 91; 66; 67; 79; 32; 35; 49]. Several studies have delved into semantic synthesis through two methodologies. One methodology [90; 28; 72; 6; 68] based on GAN and trained with adversarial loss and reconstruction loss. However, some of these methods can only generate unimodal outputs. Although some methods [67; 92] have been developed to address the diversity issues, GAN-based frameworks typically suffer from unstable training and need careful parameter tuning. Another methodology [73] employs diffusion models and regards it as a conditional image generation task, where semantic masks function as control signals. Some works further add a greater variety of control signals to enhance the consistency of synthesized results, like textual prompts [78] and bounding box [36]. Despite these methods achieves good synthetic results, their architecture is usually asymmetric, and the generator is usually unidirectional. This hinders the exploration of the unification of semantic segmentation and image synthesis.
3 Method
In this section, we first review diffusion models and the differential equations of diffusion-based segmentation models (DSMs) and then analyze the disadvantages of existing approaches. Afterward, we propose our SemFlow, which is inspired by rectified flow theory. It solves the randomness problem in the existing DSM and unifies semantic segmentation and image synthesis with one model. We will elaborate on each phase of our method.
3.1 Diffusion Model and Segmentation Modeling.
Diffusion models are class of fikelihood-based models that define a Markov chain of forward and backward processes. In the forward process, the noise is gradually added to the real data Ty to form the noisy data 2;: q = Na(x: Vaizo, (1 - aa))),, t e [O.T]]
(I)
where og is functions of t. During training, the model cp learns to estimate the noise by minimizing the objective with L2 loss:
L = Eno
[|eo(Varaa + a(c) cz 1
(2)
In the backward process, the model starts from Gaussian noise and gradually denoises to generate realistic data [63] via,
Et /I aice(xe.t)
xt-1 var-l
+
a; ca + orez-
(3)
Voe
Luckily, Eq. 3 provides a unified solution for DDPM and DDIM, where the former belongs to an SDE modeling and the latter is an ODE modeling. We parameterized it as
Z
f(zT,o),
(4)
3

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where a controls the way of modeling:
-- y (1 (1-a--1(1- ar) arraa
DDPM DDIM
(5)
In the image generation task, zo represents the real images, and 2T represents the Gaussian noise. We extend the boundaries of Eq. 4 and apply it to semantic segmentation problems. An intuitive way is to encode the segmentation mask into colormaps and model segmentation as a conditional image generation task. Given image I, we rewrite the projection f into a formulation of conditional generation,
z f l)-
Eq. 6 formulates the existing ceffussionbbsedd segmentation models with generative modeling. How- ever, this modeling approach suffers from the following problems: 1) The randomness of initial noise and the determinism of the segmentation mask are contradictory. 2) From transmission point of view, the transfer from noise to the segmentation mask does not conform to the paradigm of semantic segmentation task, where noise is redundant. 3) The images in this approach only serve as the condition, which is non-causal in reverse transfer. Thus, the reversed transfer is a separate problem.
3.2 Unify Segmentation and Synthesis with Rectified Flow
Task- Task-sgn Framework. We employ the standard Stable Diffusion [58] (SD) framework for our task without any task-specific decoder head well-designed text prompts. To this end, we design the network architecture using the following three steps. First, we convert the semantic segmentation masks to 3-channel pseudo mask M (Ma, m1, m2) align with the images I. Assume that the valid region [o, 255] (for real images) is divided into l parts with a spacing of s, the pseudo mask corresponding to category index is formulated as:
m/j k2/k2] J. m² L(c- m' //k],,
miz
c- m/ 3 mm *k, M s* (m/g m'j m2), (7)
where s * (k- 1) < 255 and |-] means the floor operator. The (m). m mb) are called anchors.
After the transformation, we adopt VAE encoder & to compress the images and pseudo masks into the latent space. The corresponding VAE decoder 'D restores the latent variables to the pixel space.
20 = E()), 21 = E(M),
i- D(E)) M D(E)),
(8)
where 2 means the output of the UNet.
Discussion, Although previous works [69] argue that segmentation masks are lower in entropy and specifically re-train a lighter network, we still adopt the off-the-shelf VAE from SD. The reasons are as follows: 1) The number of parameters in VAE is negligible compared to the UNet (84M vs. 860M). 2) The VAE specifically trained for segmentation masks can not be applied to images, thus destroying the bi-directional transportation. 3) Specific training creates spatial priors, such as clustering, which hinders our exploration of LDM's segmentation capability itself.
Note that we do not use image captions or image features prompts. As our model unifies semantic segmentation and image synthesis with one model, the usage of captions contradicts the definition of semantic segmentation task while the features non-causal for image synthesis. Thus, in this work, we set the prompt as empty.
Bi-directional Training and Inference. Contrary to the conventional approach, we propose modeling the segmentation task with rectified flow. an ODE framework that aims learn the mapping between two distributions through straight trajectories.
Denote To and m represent the distribution of the latent variables of images and masks, respectively. Denote 2g ~ Fg and z ~ Ti, the trajectory from 2p to 21 can be formulated as 2, (2x 21);
dz app (20, 21)
dt
When yo is the trajectory of rectified flow [40], 2, can be reformulated as the linear interpolation process between 2g and as 2 (1 - (1-t) + t21. We aim to learn the velocity field using neural

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networks v0(2, t) and solve with optimization methods,
% E (c no(2).t) (20 21)
dt,
(10)
Ot
L (s [110(2e: () (21 z0)11²] de,
where y indicates the coupling of images and their corresponding pseudo masks. Eq. 10 our training loss. Upon training completed, the transfer from žg 21 can be described via an ODE:
dæt = uo(2,, t), E [].
(11)
dt
So far, we have constructed a mapping from the distribution of images to that of masks. Compared with DSMs in Eq. 6, our approach avoids the interference of randomness, enabling the application of diffusion models to semantic segmentation tasks.
Moreover, Eq. 10 has time-symmetre form, which results in an equívalent problem by exchanging 2g and 21 and flipping the sign of ng. Interestingly, the transportation problem from лं to mo indicates the semantic image synthesis task. This means that semantic segmentation and semantic image synthesis essentially become a pair of mutually reverse problems that share the same ODE (Eq. 11) and have solutions with opposite signs.
In the inference stage, we can obtain the approximate results by numerical solvers like the forward Euler method, which can be formulated as follows,
Semantic segmentation is regarded as the transportation from 2g to 21, which call forward The ODE is Eq. 11 and the numerical solution is,
ス = + N va( t), t 1o., - 1J/N.
(12)
After M is restored with Eq. 8, we calculate the L2 distance between M and anchors and obtain the segmentation mask.
Correspondingly, the semantic image synthesis task is considered to transfer in reverse direction, which we call the reverse flow. Specifically, this transfer can be described as dz, u (2,, t), and the solution is,
dt
2 x/2
2t
vo(2,tt, te (N, 1,... 1)/N.
(13)
3.3 Finite Perturbation
In Eq. 10, the model is configured to learn the one-to-one mapping between images and masks. However, assigning fixed mask to each image brings about several problems. First, find that constant 2 in Eq. 13 hinders the multi-modal generation for the image synthesis task. Moreover, the pseudo masks are low in entropy. We hypothesize that the low-entropy distribution of masks hinders the training process and may finally spoil the quality of synthesis results.
To this end, propose add finite perturbation on the pseudo masks. Specifically, given pseudo masks M which has a spacing of s, we add noise with a limited amplitude on M,
M' M + ee,
U(-B,8).
(14)
where U is uniform distribution. We set 0 < s/2 to ensure that the semantic label of each pixel does not change. Therefore, we propose to replace 21 with 2 = (M'') in Eq. 10 and Eq. 13. We show the effectiveness of this design Sec. 4.3.
4 Experiments
4.1
Experimental Settings
Dataset and Metrics. We study SemFlow using three popular datasets: COCO-Stuff [37], CelebAMask-HO [30], and Cityscapes [12]. They contain 171, 19, and 19 categories, respec- tively. For semantic segmentation, we evaluate with mean intersection over union (mloU). For
5

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Table Semantic segmentation results on COCO-Stuff dataset. SS and SIS represents semantic segmentation and semantic image synthesis, respectively. Sampler-N means the usage of a specific sampler with N inference steps.
Task SS
COCO-Stule mloU (SS)
CelebAMask HQ FID (SIS) LPIPS (SIS)
Method
Sampler
SIS
MaskFormer [11]
41.9
DSM [58]
DDIM-200 DDPM-200
16.1
DSM [58]
20.2
Hix2pixHD [72]
54.7
0.529
SPADE [53]
42.2
0.487
SC-GAN [74]
19.2
0.395
BBDM [31]
BBDM-200
21.4
0.370
SemFlow (ours)
Euler-25
38.6
32.6
0.393
semantic image synthesis, we assess with the Fréchet inception distance (FID) [24] and learned perceptual image patch similarity (LPIPS) [84].
Implementation Details. The SemFlow model is built upon Stable Diffusion UNet and initialized with weights from the pre-trained SD 1.5. Images and semantic masks COCO-Stufi CelebA.Mask- HQ. and Cityscapes are resized and cropped into 512 x 512. 512 x 512, and 512 x 1024, respectively. We use the off-the-shelf VAE of the corresponding Stable Diffusion model. The spacing is set as 50, and the division coefficient& & is 6. The amplitude of perturbation is 6. Note that there is no need to train two models for segmentation and synthesis separately since the optimization target in Eq. 10 is time-symmetric.
Baselines. We seek unify semantic segmentation (SS) and semantic image synthesis (SIS) into a pair of reverse problems and train one model for a solution. As few previous works achieve this goal, we thus take different baselines for SS and SIS, respectively. For SS, we design two baseline models, DSMs [58], which follow the principle of diffusion- bbaed conditional generation modeling in Sec. 3.1. The network structure and hyperparameters of DSM follow SemFlow, except that the inputs of UNet are eight channels. Specifically, the noise and images are concatenated in the channel dimension. DSM-DDIM and DSM-DDPM differ in differential equation modeling (ODE vs. SDE). For SIS, we take pix2pixHD [72], SPADE [53], SC-GAN [74], BBDM [31] and CycleGAN [90] as the baselines.
4.2 Main Results
Semantic Segmentation. Fig. 2 shows the qualitative comparison between SemFlow and DSMs. Our SemFlow demonstrates satisfactory performance in a range of scenarios and exhibits high accuracy in classifying the semantic labels of targets. In contrast, DSM fails in semantic segmentation tasks, regardless of SDE or ODE modeling. First, DSM is inferior to SemFlow in discriminating different semantic categories. Moreover, the outputs of DSM-DDIM and DSM-DDPM change dramatically with different random seeds. As discussed in Sec. 3.1, DSM is susceptible to the randomness inherent in diffusion models, making unable to produce deterministic results.
Tab. I shows the quantitative results on the COCO-Stuff dataset. We compare SemFlow with two variants of DSM and MaskFormer, which is classical discriminative segmentation model. Regarding accuracy, our SemFlow achieves 38.6 mloU and outperforms DSMs by a remarkable margin. Moreover, SemFlow only uses simple sampler. forward Euler method, and fewer inference steps than DSMs. Further reducing the inference steps brings about faster generation but witnesses a slight drop in performance, which is analyzed in Sec. 4.3.
Semantic Image Synthesis. We compare our approach with other specialist models on semantic image synthesis tasks in Tab. 1. On CelebAMask-HO, SemFlow achieves performance of 32.6 FID and 0.393 LPIPS.
Beyond specialist models, we also qualitatively compare our approach with CycleGAN [90] in Fig. to demonstrate the overall performance on SS and SIS tasks. All results of SemFlow are generated with one model. In other words, the ODE modeling of SS and SIS share the same velocity

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Image
Ground Truth
DSM DDPM
(d) DSM DDIM
SemFloow (ours)
Figure 2: Semantic segmentation results on COCO-Stuf' dataset. For the ground truth, each color reflects the value of anchors (Eq. 7), which corresponds one semantic category. and the color white indicates the ignored regions. The predictions DSM vary considerably under different random seeds.
(i) Imput
(b) Image: : Ground Trush
(c) CycleGAN
( SemFlow (curs)
Figure 3: Semantic segmentation and semantic image synthesis results on Cityscapes dataset. The color black in the ground truth indicates the ignored region. The segmentation results SemFlow are colored following [12].
field and only differ the sign. The first and third rows show the image synthesis results given semantic layouts, while the second and fourth row shows the segmentation results. Our synthesis and segmentation results are inspiring and significantly outperform CycleGAN. Note that CycleGAN essentially trains two unidirectional generators while we employ only one model for the two tasks.

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(a) Mask
(b) w/o Perturbation
(c) Pestuutation
Figure 4: Semantic image synthesis results CelebAMask-HO dataset. Semantic masks colored to show different semantic components. SemFlow w/ Perturbation indicates the finite perturbation operation in Eq. 14.
Discussion. Although the performance gap exists compared with specialist models, our approach solves the two major issues of diffusion-basce segmentation approaches: 1) Randomness of outputs and 2) Large inference steps. We believe it significantly reduces the gap between discriminative models and diffusion models.
4.3 Ablation Studies
Perturbation. Fig. shows the synthesized results SemFlow on the CelebAMask-Ho dataset and demonstrates the importance of perturbation operation. First, perturbation enables approach generate multi-modal results from one semantic layout using different noises. The synthesized results show diverse appearances, such skin, hair color, and the background, and exhibit good consistency with the masks. Moreover, we also show the synthesis results the model without perturbation in Fig. It witnessed that the model without perturbation is only able to generate uni-modal results, and the synthesized images exhibit a loss of detail and suffer from severe over-smoothing problems.
Straight Trajectory. Our SemFlow aims to establish linear trajectories between the distribution of images and the masks, which enables it to sample with fewer steps.
Tab. 2 compares the performance of DSM and SemFlow on segmentation tasks under different inference steps, where DSM sampled with DDPM and DDIM represent SDE and ODE modeling, respectively. Overall, SemFlow outperforms DSM by remarkable margin regardless of the inference steps. Specifically, the DSMs' performance declines markedly as the number of steps decreases. With 5 steps, the DSM-DDPM achieves mloU of 12.3, while the DSM-DDIM achieves 9.5 mloU. On the contrary, our SemFlow achieves 28.3 even with one step.
Fig. provides semantic image synthesis results with different inference steps. Although fewer steps will result some loss of detail and make the images appear smoother, the results one-step synthesis are still competitive. This indicates that the trajectory between the two distributions is straightened. Fig. 6 and Fig. 7 visualizes the latent variable sampled from the trajectory. The transition between and is smooth.
5 Conclusion
In this work, we present SemFlow, a framework that employs diffusion model to integrate semantic segmentation and semantic image synthesis pair of reverse problems. To overcome the con-

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Table Semantic segmentation results with different inference steps on COCO-Stuff dataset. mloU is used as the metric.
Method&SSmmpler
1
2
5
10
25
50
100
200
DDIM
0.1
4.0
9.5
13.6
14.9
15.7
16.1
DSM
DDPM
0.1
5.3
12.3
17.5
18.9
19.6
20.2
SemFlow
Euler
28.3
31.0
36.9
38.4
38.6
38,4
38.3
38.3
N=
N=
N-10
N=
N-30
Figure 5: Image synthesis results with different inference steps. We use the forward Euler method to get numerical solutions. Our approach obtains competitive results even with only one inference step.
Figure 6: Visualization of latent variables the trajectory from 2g (Semantic image synthesis). Top row: COCO-Stuff. Bottom row: Cityscapes.
I-0
Figure 7: Visualization of latent variables on the trajectory from zo to 2 (Semantic segmenta- tion). Top row: COCO-Stuff. Bottom row: Cityscapes.
tradiction between the randomness of diffusion models and the certainty of semantic segmentation transport problem between image and mask
results, propose to model semantic segmentation distributions. We then employ rectified flow to learn the transfer function, which brings the benefits of reversible transportation. We propose finite perturbation method to enable multi-modal generation, which also greatly improves the quality of synthesized results. With straight trajectory modeling, model can sample with much fewer steps. Experimental results show that even with weak sampler, our model still achieves comparable or even better results than specialist models. We hope research can inspire the findings unified generative model design for the community.
Acknowledgement. This work was supported by the National Key Research and Development Program of China (No. 2023YFC3807600).

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Overview. In this supplementary, we present more results and details:
A. More details on our method.
B. More empirical studies and visual results.
C. Discussion of the limitations, broader impacts and safeguards.
A More Details on Method
Amplitude of Perturbation. In the main paper, the perturbation follows the uniform distribution < U)),88). We < 3 < 8/2 to prevent the semantic labels from changing. Here the proof.
Let M = (mo, , m2) be the anchor for category C1. Af' = M + e be the anchor with perturbation, and (po.P1. P2) be another anchor for category c2 C1 c2. First, it is obvious that E(M')
E(M) = M, which means that adding perturbation will not change the estimation of original anchors. Then we only need to prove || M112 < ||M' 2112, which is equivalent Eie(s) of
(E + m, - p.))². and can be further written as 0 < Eiepy (m; P.)
+ 26,). Since
< 2c, < and m, Pt can only take the values of [.... -2s, ss, 0, 2s, ...,. the two terms must have the same sign or one of them equals O. The proof is completed.
Implementation Details. We train CelebAMask-HO and Cityscapes with a batch size of 256 with A optimizer for 80K and 8K steps, respectively. The initial learning rate is set as 2 x 10-5 and 5 x 10-5 Linear learning rate scheduler is adopted. For COCO-Stuff dataset, we use constant learning rate of x 10-5 with a batch size of 128 for 320K steps. The COCO-Stuff indicates the version of COCO-Stuff-164..
B More Empirical Studies and Visual Results
Sampling from Other Distributions. Fig, 8 shows the synthesized images which sampled with different perturbations ~ U(-3', g.).. can be observed that the model can obtain high-quality synthetic results only when the perturbations in the inference stage and the training stage follow the same distribution. Specifically, the synthesized images are dim when 8 < 8, and overexposed when 3' B.
(a) Mask
(b) = 0.75B
(c) f' = B
(d) B' = 1.25
Figure 8: Image synthesis results sampled from other distributions. We sample with different
perturbation E ~ U(-3'33)) In the training stage, the perturbation follows U)-
More Visual Results on One-step Generation. Fig. shows that our model can generate competitive images with only one inference step.
Selection ODE solvers. Fig. provides visualization results on different ODE solvers. stronger solver has the potential to bring about better results.
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Figure 9: Synthesized images with inference step.
(a) Euler
(b) RK45
Figure 10: The influences of ODE solvers. (a) Euler indicates sampling with culer-25 solver. (b) RK45 indicates the Kange-Kutta method of order 5(4).
More Visual Results on Cityscapes. Fig. 11 shows the results of multi-modal image synthesis. The appearance of the synthesized scene varies according to different random seeds. Moreover, our model can learn the laws of shadows and light angles (the third column), demonstrating its great potential.
Fig. 12 shows visual results of semantic segmentation. Our model accurately segments the objects and assigns the correct semantic labels.
C Discussion
Limitations. Some previous work, such as Stable Diffusion, SDXL show that scaling up the training data is essential to exploit the potential of diffuusion models fully. Due to the limited computational resources and the number image-mask pairs the existing dataset, we leave it to future work. In addition, although this paper does focus the network structure and the design of ODE solvers, we believe there is room for exploration to further improve performance.
Broader Impacts. Our SemFlow extends the diffusion model from the generative domain to the segmentation task and narrows the gap with traditional discriminative models. It also functions as unified framework to bind semantic segmentation and image synthesis. We hope this will motivate people to explore the unification of low-level and high-level vision. In terms of social impact, will encourage artistic content creation, but at the same time may face the problem of fake content.
Safeguards. The content produced by generative model is highly correlated with its training data. Ensuring fair and clean training data can effectively prevent models from generating harmful content.
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Figure 11: Image synthesis results on Cityscapes. We show the results under three random seeds for each semantic mask. The first row: semantic layouts. The second to the fourth row: synthesized results.
(a) Image
Ground Truth
Prediction
Figure 12: Semantic segmentation results on Cityscapes. The color black in the ground truth indicates the ignored regions.
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Reviews:
[{"review_id": "wpYFSC1065", "reviewer": "Reviewer_3dM2", "summary": "This paper proposed a unified diffusion-based framework for semantic segmentation and semantic image synthesis. The proposed SemFlow applied the existing ordinary differential equation (ODE) model and modified the transport problem setting. Additionally, it incorporates techniques such as perturbation and straight trajectory to enhance model performance. The proposed method was compared with a simple diffusion-based conditional generation modeling and a transformer-based method (Mask2Former) for semantic segmentation, as well as several GAN-based and diffusion-based methods for semantic image synthesis. However, the results did not surpass existing methods, and performance in the semantic segmentation task was even 10% lower in mIoU compared to basic segmentation methods.", "questions": "Although I appreciate the motivation and exploration in this paper, the results do not convince me that the proposed method is promising and practical for image synthetic and semantic segmentation tasks.", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The motivation behind this paper is well though out. It adds value by attempting to unify low-level and high-level vision tasks. \n2.The writing style is clear and easy to understand.", "weaknesses": "1. The literature review is insufficient and lacks citations of relevant works such as FreeMask, NeurIPS, 2023. \n2. Although the motivation is thoughtful, the theoretical and practical value of the proposed method is limited. The application results are not promising, as the semantic segmentation performance is over 10% lower than Mask2Former. The method does not demonstrate advantages over existing training data synthesis methods. \n3. The key components of the proposed method are commonly used in generative fields and therefore lack novelty. \n4. The experiments are insufficient. It is recommended that the authors include FreeMask and other relevant methods for comparison in the semantic segmentation task, as well as ControlNet or Freestyle generation methods for semantic image synthesis. Additionally, the authors should provide complete quantitative results on all three datasets for both semantic image synthesis and semantic segmentation tasks. \n5. The authors claim limited computational resources as a reason to leave training data synthesis methods for future work, yet the experiments were conducted on 8 NVIDIA A100 GPUs, which is more than the resources used in most training data synthesis studies. Also, the computational cost advantages are unclear due to the absence of computation time data.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing the motivation and exploration of our work.\n\nQ1: Lack of citation and comparison with FreeMask in semantic segmentation task.\n\nA1: Thanks for pointing out this. We will cite FreeMask. However, we would like to emphasize that FreeMask is a framework for training data generation, which serves as an augmentation for existing semantic segmentation models, such as Deeplab. FreeMask resorts to synthetic images with an off-the-shelf image synthesis model, FreestyleNet, to enlarge the volume of training data. On the other hand, as stated in the title of our paper, we present a new generative method to bridge semantic segmentation and image synthesis via rectified flow. Therefore, Freemask is totally different from our proposed method in that it has different targets and motivations.\n\nQ2: Novelty issues. \n\nA2: First, we are the first to propose to unify semantic segmentation and semantic image synthesis via rectified flow. Our model first accomplishes **uni-directional training, bi-directional inferencing**. Our approach is simple yet effective without introducing extra components on existing baseline, stable diffusion models. To the best of our knowledge, we are the first to achieve this goal of seamless transformation between images and segmentation masks. Second, our approach greatly improves the performance and inference speed of LDM-based segmentation. Third, we propose finite perturbation to enable multi-modal generation and improve the quality of synthesis results. We think our contributions should not be underestimated. Moreover, other reviewers find our work interesting and novel.\n\nQ3: Performance issues. \n\n\nA3: First, we discuss the performance issues from two perspectives. For segmentation, our model does not rely on strong backbones for feature extraction or task-specific decoder like Mask2Former. For image synthesis, our model needs to establish the transmission from masks to images, rather than from noise to images, which means our model cannot use the transmission capability of Stable Diffusion itself.\n\nSecond, we compared SemFlow with Freestyle and ControlNet on ade20k. We use the provided checkpoint from Freestyle and ControlNet for ade20k dataset. Please note that our model does not take text prompts as inputs, so we report two values of Freestyle, respectively, with and without text prompts. Due to the limitation of computational resources, we do not conduct experiments of SemFlow with text prompts.\n\n| Method | Freestyle w/o text | Freestyle w/ text | ControlNet w/ text | ours |\n|---|---|---|---|---|\n| FID $\\downarrow$ | 164.5 | 25.0 | 52.1 | 27.8 |\n\nWe also use the same model and compare it with MaskFormer on ade20k semantic segmentation task. \n\n| Method | MaskFormer | ours |\n|---|---|---|\n| mIoU $\\uparrow$ | 44.5 | 41.0 |\n\nQ4: 8 NVIDIA A100 GPUs are more than the resources used in most training data synthesis studies. Computation time.\n\nA4: We argue that our task is not **training data synthesis**. Our model needs to establish the reversible transport mapping between images and semantic masks. However, the transport of Stable Diffusion (SD) is between noises and images. As a result, our model cannot use the transport capability of SD. The creation of the mapping is difficult. For example, the training of InstaFlow costs around 199 A100 days. We train SemFlow on CelebAMask for around 37 hours.", "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": "nBfASqugTi", "reviewer": "Reviewer_5PqV", "summary": "The paper presents SemFlow, an approach that binds semantic segmentation and semantic image synthesis using an ordinary differential equation (ODE) model. The motivation is to use rectified flow to enable LDM as a unified framework for both tasks. The key contributions include a unified framework that jointly optimizes both tasks, the specialized designs of the frameworks, including pseudo mask modelling, bi-directional training of segmentation and generation, and a finite perturbation strategy. This approach bridges the gap between semantic segmentation and semantic image synthesis, showing good visualization results.", "questions": "See Weaknesses", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The unified framework for joint optimization of semantic segmentation and semantic image synthesis is novel.\n\n2. The paper is generally well-written and structured.", "weaknesses": "1. Lines 133-140: Why is there a necessity to transform the semantic segmentation masks into 3-channel pseudo-masks utilizing Eq. 7? Could you provide insights on how the formulations for m1 and m2 were derived?\n\n2. Figure 4: During the model inference process (semantic image synthesis task), will noise be added to the mask? \n\n3. Lines 147-155: SemFlow cannot use captions to guide image synthesis, and the authors claim the usage of captions is non-casual for semantic image synthesis, however, there is still some work on it [1,2].\n\n4. There is still a gap in quantitative results compared to the popular model within each task.\n\n[1] Xue, Han, et al. \"Freestyle layout-to-image synthesis.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2023.\n\n[2] Lv, Zhengyao, et al. \"Place: Adaptive layout-semantic fusion for semantic image synthesis.\" *Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition*. 2024.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing our strengths: The unified framework for joint optimization of semantic segmentation and semantic image synthesis is novel. We provide more clarifications below.\n\nQ1: The necessity of 3-channel pseudo-masks and the insights of Eq.7.\n\nA1: The mask needs to be converted into a 3-channel pseudo mask to align with the VAE, which takes as input a 3-channel tensor. Eq.7 is inspired by K-based numbers. In this encoding method, the 3-channel encoding space can represent ${K}^3$ anchors, and the distance between each anchor is greater than $s$. This approach can approximately maximize the utilization of the encoding space. \n\nQ2: Will noise be added to the mask in the semantic image synthesis task?\n\nA2: Yes. The distribution of masks in the inference stage must follow that in the training stage. Also, the noise is a necessity for multi-modal generation. We also conduct ablation experiments in the supplementary Sec. B (Fig.7), which shows that sampling from a different distribution (aka., different noise) brings about significant performance degradation.\n\nQ3: Clarification of \"captions\" in L147-155.\n\nA3: Sorry for confusion. In L147-150, we wrote, \"...we do not use image captions or image features as prompts...the latter is non-casual for image synthesis\". The \"latter\" means \"image features\". We will revise it to \"the image feature is non-causal for image synthesis\".\n\nQ4: Performance issues.\n\nA4: \n1. For semantic segmentation, our model does not use extra feature extractors because they destroy the transport's symmetry.\n2. From the transport perspective, our model needs to establish the reversible transport mapping between images and masks. However, the mapping of Stable Diffusion is from noises to images. This means that our model cannot use SD's transport capability, so it is a harder task for our model in the image synthesis task.\n3. Our method can greatly improve diffusion-based segmentation methods' performance and inference speed even with a simple Euler sampler following [1]. A higher-order sampler has the potential to bring about better results. Here is the comparison on the ade20k dataset,\n\n| Sampler | Euler | RK45 |\n|---|---|---|\n| FID $\\downarrow$ | 39.2 | 27.8 |\n\n[1] Liu, Xingchao, et al. \"Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow\". ICLR, 2023.", "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": "UEB9ZFXdLS", "reviewer": "Reviewer_eo5D", "summary": "This paper presents a work for solving semantic image segmentation and image synthesis simultaneously. This work proposed to use rectified flow and adopt a VAE encoder to compress the images and pseudo masks into the latent space. By comparing the proposed method with previous semantic segmentation models and image synthesis SOTAs, the effectiveness of this method is demonstrated. The proposed method handles the randomness issue for semantic segmentation. Finally, ablation study has been provided.", "questions": "See above.", "limitations": "No.", "rating": 5, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "+ This proposed an interesting formulation to bridge semantic segmentation and image synthesis in the stable diffusion framework with rectified flow framework. It is an interesting work and different to previous work on unifying semantic segmentation and image synthesis, which produces segmentation masks and synthesized images at the same time. Differently, this work trains one model to convert between segmentation masks and synthesized images.\n\n+ This work also shows faster generation speed for high quality images.", "weaknesses": "- What is the motivation to use Euler sampler. More discussion between Euler and DDIM/DDPM will be more helpful to understand the technical details for most readers.\n\n- For image synthesis task, the proposed method had a clear gap compared with other diffusion models.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing our strengths: 1. Our work bridges semantic segmentation and image synthesis with rectified flow framework. 2. Our work shows faster generation speed for high-quality images. We provide more clarifications below.\n\nQ1: The motivation to use the Euler sampler. More discussion between Euler and DDIM/DDPM.\n\nA1: Rectified flow (RF) has one type of modeling, ODE, and diffusion models (DMs) have two types of modeling, SDE and ODE, respectively. We aim to discuss all of these modeling methods. To this end, we use the Euler sampler for SemFlow (RF, ODE) following [1] and DDIM for DSM (DM, ODE) following [2]. Eq.3 provides a unified solution for SDE/ODE modeling of diffusion models, so we adopt DDPM for DSM (DM, SDE). In the context of ODE solvers, DDIM is slightly better as it fully utilizes the semi-linear structure of diffusion ODEs[3]. \n\n\nQ2: Performance gap compared with other diffusion models.\n\nA2:\n1. Our model needs to establish the reversible transport mapping between images and masks. This means it cannot use the transport capability of Stable Diffusion, which is pre-trained on a large image-text dataset and has built stable mappings between noises and images. \n2. We aim to show that our method can significantly improve the performance and inference speed of diffusion-based segmentation methods. To this end, we follow [1] and only use a simple Euler sampler in segmentation and synthesis tasks. A higher-order sampler has the potential to bring about better results. Here is the comparison on the ade20k dataset,\n\n| Sampler | Euler | RK45 |\n|---|---|---|\n| FID $\\downarrow$ | 39.2 | 27.8 |\n\n[1] Liu, Xingchao, et al. \"Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow.\" ICLR. 2023.\n\n[2] Qi, Lu, et al. \"Unigs: Unified representation for image generation and segmentation.\" CVPR. 2024.\n\n[3] Lu, Cheng, et al. \"Dpm-solver: A fast ode solver for diffusion probabilistic model sampling in around 10 steps.\" NeurIPS. 2022.", "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:
## Global Response

We thank all the reviewers for their insightful reviews. We first summarize the strengths of our paper that the reviewers recognized.
1. The unified framework of bridging semantic segmentation and image synthesis via rectified flow is interesting and novel.
2. This work shows faster generation speed for high-quality images.
3. This work adds value by attempting to unify low-level and high-level vision tasks.

Next, we aim to re-elaborate our contributions and address common concerns raised by reviewers.

**Contributions**

This work proposes a unified framework that models semantic segmentation and image synthesis as a pair of reverse problems. We are the first to propose symmetric modeling of segmentation and generation to accomplish **uni-directional training, bi-directional inferencing**. 
For semantic segmentation, our approach solves the contradiction between the randomness of diffusion outputs and the uniqueness of segmentation results. It also greatly improves the accuracy and inference speed of diffusion-based segmentation methods.
For image synthesis, we propose a finite perturbation approach to enable multi-modal generation and improve the quality of synthesis results.

**Performance Gap**

Our model aims to establish a reversible transport mapping between the distribution of images and masks. First, for segmentation tasks, we do not use specifically designed backbones for feature extraction (e.g., ResNet, ViT) because they destroy the symmetry of the transport. 
Second, Stable Diffusion is pre-trained on large text-image datasets and thus has a strong capability to transport from noises to masks. As a result, diffusion-based methods like Freestyle are easier to obtain good results than to re-establish the mapping. 
Finally, we only use a simple Euler sampler to compare fairly with DDIM, a 1-order ODE solver commonly used in diffusion-based segmentation like UniGS[1]. A higher-order sampler has the potential to obtain a more precise estimation of the trajectory and achieve better results.

[1] Qi, Lu, et al. "Unigs: Unified representation for image generation and segmentation." CVPR. 2024.

Meta-review: This paper proposes a new unified framework that binds semantic segmentation and image synthesis with rectified flow as a pair of reverse problems, trained with an ordinary differential equation (ODE) model to transport between the distributions of real images and semantic masks, using techniques including pseudo mask modeling, bi-directional training of segmentation and generation, and a finite perturbation strategy.

It has received 1x borderline reject and 2x borderline accepts.  Authors have provided an extensive rebuttal which has partially addressed most concerns.  Reviewers generally like the motivation to unify two different tasks in a reversible process,  with "uni-directional training, bi-directional inferencing".  Reviewers questions the extent of technical novelty and performance gaps, esp. on segmentation (10% worse than Mask2Former).  While authors explains the cause of this gap by pointing out that their model cannot leverage the transport capability of Stable Diffusion between noises and images for the transport between images and masks,  this inability does cast doubts on the flexibility and practicality of this framework. 

Nevertheless, the AC recommends acceptance based on the consensus of an interesting novel approach to unify low-level and high-level vision tasks, with non-trivial technical solutions.  Please take all the comments and additional clarification/results in the rebuttal into account and improve the quality in the final version.
Decision: Accept (poster)