Multimodal Unsupervised Image-to-Image Translation · Translation (MUNIT) framework. We assume that...

Multimodal UnsupervisedImage-to-Image Translation

Xun Huang1, Ming-Yu Liu2, Serge Belongie1, Jan Kautz2

Cornell University1 NVIDIA2

Abstract. Unsupervised image-to-image translation is an important andchallenging problem in computer vision. Given an image in the sourcedomain, the goal is to learn the conditional distribution of correspond-ing images in the target domain, without seeing any examples of corre-sponding image pairs. While this conditional distribution is inherentlymultimodal, existing approaches make an overly simplified assumption,modeling it as a deterministic one-to-one mapping. As a result, they failto generate diverse outputs from a given source domain image. To addressthis limitation, we propose a Multimodal Unsupervised Image-to-imageTranslation (MUNIT) framework. We assume that the image represen-tation can be decomposed into a content code that is domain-invariant,and a style code that captures domain-specific properties. To translatean image to another domain, we recombine its content code with a ran-dom style code sampled from the style space of the target domain. Weanalyze the proposed framework and establish several theoretical results.Extensive experiments with comparisons to state-of-the-art approachesfurther demonstrate the advantage of the proposed framework. Moreover,our framework allows users to control the style of translation outputs byproviding an example style image. Code and pretrained models are avail-able at https://github.com/nvlabs/MUNIT.

Keywords: GANs, image-to-image translation, style transfer

1 Introduction

Many problems in computer vision aim at translating images from one domain toanother, including super-resolution [1], colorization [2], inpainting [3], attributetransfer [4], and style transfer [5]. This cross-domain image-to-image transla-tion setting has therefore received significant attention [6–25]. When the datasetcontains paired examples, this problem can be approached by a conditional gen-erative model [6] or a simple regression model [13]. In this work, we focus on themuch more challenging setting when such supervision is unavailable.

In many scenarios, the cross-domain mapping of interest is multimodal. Forexample, a winter scene could have many possible appearances during summerdue to weather, timing, lighting, etc. Unfortunately, existing techniques usuallyassume a deterministic [8–10] or unimodal [15] mapping. As a result, they failto capture the full distribution of possible outputs. Even if the model is madestochastic by injecting noise, the network usually learns to ignore it [6, 26].

https://github.com/nvlabs/MUNIT

2 Xun Huang, Ming-Yu Liu, Serge Belongie, Jan Kautz

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(a) Auto-encoding (b) Translation

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Fig. 1. An illustration of our method. (a) Images in each domain Xi are encoded to ashared content space C and a domain-specific style space Si. Each encoder has an inversedecoder omitted from this figure. (b) To translate an image in X1 (e.g., a leopard) toX2 (e.g., domestic cats), we recombine the content code of the input with a randomstyle code in the target style space. Different style codes lead to different outputs.

In this paper, we propose a principled framework for the Multimodal UNsu-pervised Image-to-image Translation (MUNIT) problem. As shown in Fig. 1 (a),our framework makes several assumptions. We first assume that the latent spaceof images can be decomposed into a content space and a style space. We furtherassume that images in different domains share a common content space but notthe style space. To translate an image to the target domain, we recombine itscontent code with a random style code in the target style space (Fig. 1 (b)). Thecontent code encodes the information that should be preserved during transla-tion, while the style code represents remaining variations that are not containedin the input image. By sampling different style codes, our model is able to pro-duce diverse and multimodal outputs. Extensive experiments demonstrate theeffectiveness of our method in modeling multimodal output distributions andits superior image quality compared with state-of-the-art approaches. Moreover,the decomposition of content and style spaces allows our framework to performexample-guided image translation, in which the style of the translation outputsare controlled by a user-provided example image in the target domain.

2 Related Works

Generative adversarial networks (GANs). The GAN framework [27] hasachieved impressive results in image generation. In GAN training, a generator istrained to fool a discriminator which in turn tries to distinguish between gener-ated samples and real samples. Various improvements to GANs have been pro-posed, such as multi-stage generation [28–33], better training objectives [34–39],and combination with auto-encoders [40–44]. In this work, we employ GANs toalign the distribution of translated images with real images in the target domain.

Image-to-image translation. Isola et al. [6] propose the first unified frame-work for image-to-image translation based on conditional GANs, which has beenextended to generating high-resolution images by Wang et al. [20]. Recent stud-ies have also attempted to learn image translation without supervision. This

Multimodal Unsupervised Image-to-Image Translation 3

problem is inherently ill-posed and requires additional constraints. Some worksenforce the translation to preserve certain properties of the source domain data,such as pixel values [21], pixel gradients [22], semantic features [10], class labels[22], or pairwise sample distances [16]. Another popular constraint is the cycleconsistency loss [7–9]. It enforces that if we translate an image to the target do-main and back, we should obtain the original image. In addition, Liu et al. [15]propose the UNIT framework, which assumes a shared latent space such thatcorresponding images in two domains are mapped to the same latent code.

A significant limitation of most existing image-to-image translation methodsis the lack of diversity in the translated outputs. To tackle this problem, someworks propose to simultaneously generate multiple outputs given the same inputand encourage them to be different [13, 45, 46]. Still, these methods can only gen-erate a discrete number of outputs. Zhu et al. [11] propose a BicycleGAN thatcan model continuous and multimodal distributions. However, all the aforemen-tioned methods require supervision in the form of input-output pairs, while ourmethod works even in the unsupervised setting.

Our problem has some connections with multi-domain image-to-image trans-lation [19, 47, 48]. Specifically, when we know how many modes each domain hasand the mode each sample belongs to, it is possible to treat each mode as a sep-arate domain and use multi-domain image-to-image translation techniques tolearn a mapping between each pair of modes, thus achieving multimodal trans-lation. However, in general we do not assume such information is available. Also,our stochastic model can represent continuous output distributions, while [19,47, 48] still use a deterministic model for each pair of domains.

Style transfer. Style transfer aims at modifying the style of an image whilepreserving its content, which is closely related to image-to-image translation.Here, we make a distinction between example-guided style transfer, in which thetarget style comes from a single example, and collection style transfer, in whichthe target style is defined by a collection of images. Classical style transfer ap-proaches [5, 49–54] typically tackle the former problem, whereas image-to-imagetranslation methods have been demonstrated to perform well in the latter [8].We will show that our model is able to address both problems, thanks to itsdisentangled representation of content and style.

Learning disentangled representations. Our work draws inspiration fromrecent works on disentangled representation learning. For example, InfoGAN [55]and β-VAE [56] have been proposed to learn disentangled representations with-out supervision. Some other works [57–64] focus on disentangling content fromstyle. Although it is difficult to define content/style and different works use dif-ferent definitions, we refer to “content” as the underling spatial structure and“style” as the rendering of the structure. In our setting, we have two domainsthat share the same content distribution but have different style distributions.


3 Multimodal Unsupervised Image-to-image Translation

3.1 Assumptions

Let x1 ∈ X1 and x2 ∈ X2 be images from two different image domains. In theunsupervised image-to-image translation setting, we are given samples drawnfrom two marginal distributions p(x1) and p(x2), without access to the jointdistribution p(x1, x2). Our goal is to estimate the two conditionals p(x2|x1)and p(x1|x2) with learned image-to-image translation models p(x1→2|x1) andp(x2→1|x2), where x1→2 is a sample produced by translating x1 to X2 (similarfor x2→1). In general, p(x2|x1) and p(x1|x2) are complex and multimodal distri-butions, in which case a deterministic translation model does not work well.

To tackle this problem, we make a partially shared latent space assumption.Specifically, we assume that each image xi ∈ Xi is generated from a contentlatent code c ∈ C that is shared by both domains, and a style latent codesi ∈ Si that is specific to the individual domain. In other words, a pair ofcorresponding images (x1, x2) from the joint distribution is generated by x1 =G∗1(c, s1) and x2 = G∗2(c, s2), where c, s1, s2 are from some prior distributionsand G∗1, G∗2 are the underlying generators. We further assume that G∗1 and G∗2 aredeterministic functions and have their inverse encoders E∗1 = (G∗1)−1 and E∗2 =(G∗2)−1. Our goal is to learn the underlying generator and encoder functions withneural networks. Note that although the encoders and decoders are deterministic,p(x2|x1) is a continuous distribution due to the dependency of s2.

Our assumption is closely related to the shared latent space assumption pro-posed in UNIT [15]. While UNIT assumes a fully shared latent space, we postu-late that only part of the latent space (the content) can be shared across domainswhereas the other part (the style) is domain specific, which is a more reasonableassumption when the cross-domain mapping is many-to-many. In addition, weassume the content code is a high-dimensional spatial map that has a complexprior distribution instead of a simple independent Gaussian [15], since the con-tent feature encodes the complex spatial structure of the data. On the contrary,we assume the style codes are low-dimensional vectors that can be modeled byGaussian priors, since they have a global and relatively simple effect.

3.2 Model

Fig. 2 shows an overview of our model and its learning process. Similar to Liuet al. [15], our translation model consists of an encoder Ei and a decoder Gi foreach domain Xi (i = 1, 2). As shown in Fig. 2 (a), the latent code of each auto-encoder is factorized into a content code ci and a style code si, where (ci, si) =(Ec

i (xi), Esi (xi)) = Ei(xi). Image-to-image translation is performed by swapping

encoder-decoder pairs, as illustrated in Fig. 2 (b). For example, to translate animage x1 ∈ X1 to X2, we first extract its content latent code c1 = Ec

1(x1) andrandomly draw a style latent code s2 from the prior distribution q(s2) ∼ N (0, I).We then use G2 to produce the final output image x1→2 = G2(c1, s2). We notethat although the prior distribution is unimodal, the output image distributioncan be multimodal thanks to the nonlinearity of the decoder.


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(b) Cross-domain translation (a) Within-domain reconstruction

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loss

GANloss

domain 1auto-encoders

domain 2auto-encoders

stylefeatures

contentfeaturesc

s

images

Gaussianprior

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Enco

deDe

code

Enco

deDe

code

Enco

de

Fig. 2. Model overview. Our image-to-image translation model consists of two auto-encoders (denoted by red and blue arrows respectively), one for each domain. The latentcode of each auto-encoder is composed of a content code c and a style code s. We trainthe model with adversarial objectives (dotted lines) that ensure the translated imagesto be indistinguishable from real images in the target domain, as well as bidirectionalreconstruction objectives (dashed lines) that reconstruct both images and latent codes.

Our loss function comprises a bidirectional reconstruction loss that ensuresthe encoders and decoders are inverses, and an adversarial loss that matches thedistribution of translated images to the image distribution in the target domain.

Bidirectional reconstruction loss. To learn pairs of encoder and decoder thatare inverses of each other, we use objective functions that encourage reconstruc-tion in both image → latent → image and latent → image → latent directions:

– Image reconstruction. Given an image sampled from the data distribution,we should be able to reconstruct it after encoding and decoding.

Lx1recon = Ex1∼p(x1)[||G1(Ec

1(x1), Es1(x1))− x1||1] (1)

– Latent reconstruction. Given a latent code (style and content) sampledfrom the latent distribution at translation time, we should be able to recon-struct it after decoding and encoding.

Lc1recon = Ec1∼p(c1),s2∼q(s2)[||Ec

2(G2(c1, s2))− c1||1] (2)

Ls2recon = Ec1∼p(c1),s2∼q(s2)[||Es

2(G2(c1, s2))− s2||1] (3)

where q(s2) is the priorN (0, I), p(c1) is given by c1 = Ec1(x1) and x1 ∼ p(x1).

We note the other loss terms Lx2recon, Lc2

recon, and Ls1recon are defined in a similar

manner. We use L1 reconstruction loss as it encourages sharp output images.The style reconstruction loss Lsi

recon is reminiscent of the latent reconstructionloss used in the prior works [11, 31, 44, 55]. It has the effect on encouraging diverse


outputs given different style codes. The content reconstruction loss Lcirecon en-

courages the translated image to preserve semantic content of the input image.

Adversarial loss. We employ GANs to match the distribution of translatedimages to the target data distribution. In other words, images generated by ourmodel should be indistinguishable from real images in the target domain.

Lx2

GAN = Ec1∼p(c1),s2∼q(s2)[log(1−D2(G2(c1, s2)))] + Ex2∼p(x2)[logD2(x2)] (4)

where D2 is a discriminator that tries to distinguish between translated imagesand real images in X2. The discriminator D1 and loss Lx1

GAN are defined similarly.

Total loss. We jointly train the encoders, decoders, and discriminators to opti-mize the final objective, which is a weighted sum of the adversarial loss and thebidirectional reconstruction loss terms.

minE1,E2,G1,G2

maxD1,D2

L(E1, E2, G1, G2, D1, D2) = Lx1

GAN + Lx2

GAN +

λx(Lx1recon + Lx2

recon) + λc(Lc1recon + Lc2

recon) + λs(Ls1recon + Ls2

recon) (5)

where λx, λc, λs are weights that control the importance of reconstruction terms.

4 Theoretical Analysis

We now establish some theoretical properties of our framework. Specifically, weshow that minimizing the proposed loss function leads to 1) matching of latentdistributions during encoding and generation, 2) matching of two joint imagedistributions induced by our framework, and 3) enforcing a weak form of cycleconsistency constraint. All the proofs are given in the appendix.

First, we note that the total loss in Eq. (5) is minimized when the translateddistribution matches the data distribution and the encoder-decoder are inverses.

Proposition 1. Suppose there exists E∗1 , E∗2 , G∗1, G∗2 such that: 1) E∗1 = (G∗1)−1

and E∗2 = (G∗2)−1, and 2) p(x1→2) = p(x2) and p(x2→1) = p(x1). Then E∗1 , E∗2 ,G∗1, G∗2 minimizes L(E1, E2, G1, G2) = max

D1,D2

L(E1, E2, G1, G2, D1, D2) (Eq. (5)).

4.1 Latent Distribution Matching

For image generation, existing works on combining auto-encoders and GANsneed to match the encoded latent distribution with the latent distribution thedecoder receives at generation time, using either KLD loss [15, 40] or adversarialloss [17, 42] in the latent space. The auto-encoder training would not help GANtraining if the decoder received a very different latent distribution during genera-tion. Although our loss function does not contain terms that explicitly encouragethe match of latent distributions, it has the effect of matching them implicitly.

Proposition 2. When optimality is reached, we have:

p(c1) = p(c2), p(s1) = q(s1), p(s2) = q(s2)


The above proposition shows that at optimality, the encoded style distributionsmatch their Gaussian priors. Also, the encoded content distribution matches thedistribution at generation time, which is just the encoded distribution from theother domain. This suggests that the content space becomes domain-invariant.

4.2 Joint Distribution Matching

Our model learns two conditional distributions p(x1→2|x1) and p(x2→1|x2), which,together with the data distributions, define two joint distributions p(x1, x1→2)and p(x2→1, x2). Since both of them are designed to approximate the same un-derlying joint distribution p(x1, x2), it is desirable that they are consistent witheach other, i.e., p(x1, x1→2) = p(x2→1, x2).

Joint distribution matching provides an important constraint for unsuper-vised image-to-image translation and is behind the success of many recent meth-ods. Here, we show our model matches the joint distributions at optimality.

Proposition 3. When optimality is reached, we have p(x1, x1→2) = p(x2→1, x2).

4.3 Style-augmented Cycle Consistency

Joint distribution matching can be realized via cycle consistency constraint [8],assuming deterministic translation models and matched marginals [43, 65, 66].However, we note that this constraint is too strong for multimodal image trans-lation. In fact, we prove in the appendix that the translation model will degen-erate to a deterministic function if cycle consistency is enforced. In the followingproposition, we show that our framework admits a weaker form of cycle con-sistency, termed as style-augmented cycle consistency, between the image–stylejoint spaces, which is more suited for multimodal image translation.

Proposition 4. Denote h1 = (x1, s2) ∈ H1 and h2 = (x2, s1) ∈ H2. h1, h2 arepoints in the joint spaces of image and style. Our model defines a deterministicmapping F1→2 from H1 to H2 (and vice versa) by F1→2(h1) = F1→2(x1, s2) ,(G2(Ec

1(x1), s2), Es1(x1)). When optimality is achieved, we have F1→2 = F−12→1.

Intuitively, style-augmented cycle consistency implies that if we translatean image to the target domain and translate it back using the original style, weshould obtain the original image. Note that we do not use any explicit loss termsto enforce style-augmented cycle consistency, but it is implied by the proposedbidirectional reconstruction loss.

5 Experiments

5.1 Implementation Details

Fig. 3 shows the architecture of our auto-encoder. It consists of a content encoder,a style encoder, and a joint decoder. More detailed information and hyperparam-eters are given in the appendix. We will provide an open-source implementationin PyTorch [67].


Fig. 3. Our auto-encoder architecture.

Content encoder. Our content encoder consists of several strided convolutionallayers to downsample the input and several residual blocks [68] to further processit. All the convolutional layers are followed by Instance Normalization (IN) [69].

Style encoder. The style encoder includes several strided convolutional layers,followed by a global average pooling layer and a fully connected (FC) layer. Wedo not use IN layers in the style encoder, since IN removes the original featuremean and variance that represent important style information [52].

Decoder. Our decoder reconstructs the input image from its content and stylecode. It processes the content code by a set of residual blocks and finally pro-duces the reconstructed image by several upsampling and convolutional layers.Inspired by recent works that use affine transformation parameters in normal-ization layers to represent styles [52, 70–72], we equip the residual blocks withAdaptive Instance Normalization (AdaIN) [52] layers whose parameters are dy-namically generated by a multilayer perceptron (MLP) from the style code.

AdaIN(z, γ, β) = γ

(z − µ(z)

σ(z)

)+ β (6)

where z is the activation produced by the previous convolutional layer, µ and σare channel-wise mean and standard deviation, γ and β are parameters generatedby the MLP from the style code. Note that the affine parameters are produced bya learned network, instead of computed from statistics of a pretrained networkas in Huang et al. [52].

Discriminator. We use the LSGAN objective proposed by Mao et al. [38]. Weemploy multi-scale discriminators proposed by Wang et al. [20] to guide thegenerators to produce both realistic details and correct global structure.

Domain-invariant perceptual loss. The perceptual loss, often computed asa distance in the VGG [73] feature space between the output and the referenceimage, has been shown to benefit image-to-image translation when paired su-pervision is available [13, 20]. In the unsupervised setting, however, we do nothave a reference image in the target domain. We propose a modified versionof perceptual loss that is more domain-invariant, so that we can use the input


image as the reference. Specifically, before computing the distance, we performInstance Normalization [69] (without affine transformations) on the VGG fea-tures in order to remove the original feature mean and variance, which containsmuch domain-specific information [52, 74]. We find it accelerates training onhigh-resolution (≥ 512× 512) datasets and thus employ it on those datasets.

5.2 Evaluation Metrics

Human Preference. To compare the realism and faithfulness of translationoutputs generated by different methods, we perform human perceptual studyon Amazon Mechanical Turk (AMT). Similar to Wang et al. [20], the workersare given an input image and two translation outputs from different methods.They are then given unlimited time to select which translation output looksmore accurate. For each comparison, we randomly generate 500 questions andeach question is answered by 5 different workers. A worker has to have a lifetimetask approval rate grater than 98% to be able to answer the questions.

LPIPS Distance. To measure translation diversity, we compute the averageLPIPS distance [75] between pairs of randomly-sampled translation outputs fromthe same input as in Zhu et al. [11]. LPIPS is given by a weighted L2 distancebetween deep features of images. It has been demonstrated to correlate well withhuman perceptual similarity [75]. Following Zhu et al. [11], we use 100 input im-ages and sample 19 output pairs per input, which amounts to 1900 pairs in total.We use the ImageNet-pretrained AlexNet [76] as the deep feature extractor.

(Conditional) Inception Score. The Inception Score (IS) [34] is a popu-lar metric for image generation tasks. We propose a modified version calledConditional Inception Score (CIS), which is more suited for evaluating multi-modal image translation. When we know the number of modes in X2 as wellas the ground truth mode each sample belongs to, we can train a classifierp(y2|x2) to classify an image x2 into its mode y2. Conditioned on a singleinput image x1, the translation samples x1→2 should be mode-covering (thusp(y2|x1) =

∫p(y|x1→2)p(x1→2|x1) dx1→2 should have high entropy) and each

individual sample should belong to a specific mode (thus p(y2|x1→2) shouldhave low entropy). Combing these two requirements we get:

CIS = Ex1∼p(x1)[Ex1→2∼p(x2→1|x1)[KL(p(y2|x1→2)||p(y2|x1))]] (7)

To compute the (unconditional) IS, p(y2|x1) is replaced with the unconditionalclass probability p(y2) =

∫∫p(y|x1→2)p(x1→2|x1)p(x1) dx1 dx1→2.

IS = Ex1∼p(x1)[Ex1→2∼p(x2→1|x1)[KL(p(y2|x1→2)||p(y2))]] (8)

To obtain a high CIS/IS score, a model needs to generate samples that are bothhigh-quality and diverse. While IS measures diversity of all output images, CISmeasures diversity of outputs conditioned on a single input image. A model thatdeterministically generates a single output given an input image will receivea zero CIS score, though it might still get a high score under IS. We use the


Inception-v3 [77] fine-tuned on our specific datasets as the classifier and estimateEq. (7) and Eq. (8) using 100 input images and 100 samples per input.

5.3 Baselines

UNIT [15]. The UNIT model consists of two VAE-GANs with a fully sharedlatent space. The stochasticity of the translation comes from the Gaussian en-coders as well as the dropout layers in the VAEs.

CycleGAN [8]. CycleGAN consists of two residual translation networks trainedwith adversarial loss and cycle reconstruction loss. We use Dropout during bothtraining and testing to encourage diversity, as suggested in Isola et al. [6].

CycleGAN* [8] with noise. To test whether we can generate multimodaloutputs within the CycleGAN framework, we additionally inject noise vectorsto both translation networks. We use the U-net architecture described in Zhu etal. [11] with noise added to input, since we find the noise vectors are completelyignored by the residual architecture in CycleGAN [8]. Dropout is also utilizedduring both training and testing.

BicycleGAN [11]. BicycleGAN is the only existing image-to-image translationmodel we are aware of that can generate continuous and multimodal output dis-tributions. However, it requires paired training data. We compare our model withBicycleGAN when the dataset contains pair information. While BicycleGAN istrained in a supervised manner, our model never sees paired examples.

5.4 Datasets

Edges ↔ shoes/handbags. We use the datasets provided by Isola et al. [6],Yu et al. [78], and Zhu et al. [79], which contain images of shoes and handbagswith edge maps generated by HED [80]. We train one model for edges ↔ shoesand another for edges ↔ handbags without using paired information.

Animal image translation. We collect images from 3 categories/domains,including house cats, big cats, and dogs. Each domain contains 4 modes whichare fine-grained categories belonging to the same parent category. Note that themodes of the images are not known during learning the translation model. Themodes are only used to train a classifier for computing IS and CIS. We learn aseparate model for each pair of domains.

Street scene images. We experiment with two street scene translation tasks:

– Synthetic ↔ real. We perform translation between synthetic images in theSYNTHIA dataset [81] and real-world images in the Cityscape dataset [82].For the SYNTHIA dataset, we use the SYNTHIA-Seqs subset which containsimages in different seasons, weather, and illumination conditions.

– Summer ↔ winter. We use the dataset from Liu et al. [15], which containssummer and winter street images extracted from real-world driving videos.

Yosemite summer ↔ winter (HD). We collect a new high-resolution datasetcontaining 3253 summer photos and 2385 winter photos of Yosemite. The imagesare downsampled such that the shortest side of each image is 1024 pixels.


& GT

Input UNIT CycleGAN

with noise

CycleGAN*

w/o Lxrecon

MUNIT

w/o Lcrecon

MUNIT

w/o Lsrecon

MUNIT

(ours)

MUNIT

GAN

Bicycle-

Fig. 4. Qualitative comparison on edges → shoes. The first column shows the input andground truth output. Each following column shows 3 random outputs from a method.

Table 1. Quantitative evaluation on edges → shoes/handbags. The diversity score isthe average LPIPS distance [75]. The quality score is the human preference score, thepercentage a method is preferred over MUNIT. For both metrics, the higher the better.

edges → shoes edges → handbags

Quality Diversity Quality Diversity

UNIT [15] 37.4% 0.011 37.3% 0.023

CycleGAN [8] 36.0% 0.010 40.8% 0.012

CycleGAN* [8] with noise 29.5% 0.016 45.1% 0.011

MUNIT w/o Lxrecon 6.0% 0.213 29.0% 0.191

MUNIT w/o Lcrecon 20.7% 0.172 9.3% 0.185

MUNIT w/o Lsrecon 28.6% 0.070 24.6% 0.139

MUNIT 50.0% 0.109 50.0% 0.175

BicycleGAN [11]† 56.7% 0.104 51.2% 0.140

Real data N/A 0.293 N/A 0.371

† Trained with paired supervision.

5.5 Results

First, we qualitatively compare MUNIT with the three baselines above, and threevariants of MUNIT that ablate Lx

recon, Lcrecon, Ls

recon respectively. Fig. 4 showsexample results on edges → shoes. Both UNIT [15] and CycleGAN [8] (with orwithout noise) fail to generate diverse outputs, despite the injected randomness.Without Lx

recon or Lcrecon, the image quality of MUNIT is unsatisfactory due

to the lack of constraint. Without Lsrecon, the model suffers from partial mode

collapse, with many outputs being almost identical (e.g., the first two rows). Ourfull MUNIT model produces images that are both diverse and realistic, similarto BicycleGAN [11] but does not require supervision.

The qualitative observations above are confirmed by quantitative evaluations.We use human preference to measure quality and LPIPS distance to evaluatediversity, as described in Sec. 5.2. We conduct this experiment on the task of


Input GT Sample translations

(a) edges ↔ shoes

Input GT Sample translations

(b) edges ↔ handbags

Fig. 5. Example results of (a) edges ↔ shoes and (b) edges ↔ handbags.

Input Sample translations

(a) house cats → big cats


(b) big cats → house cats

(c) house cats → dogs (d) dogs → house cats

(e) big cats → dogs (f) dogs → big cats

Fig. 6. Example results of animal image translation.

edges → shoes/handbags. As shown in Table 1, UNIT and CycleGAN producevery little diversity according to LPIPS distance. Removing Lx

recon or Lcrecon from

MUNIT leads to significantly worse quality. Without Lsrecon, both quality and di-

versity deteriorate. Remarkably, the proposed MUNIT model obtains quality anddiversity comparable to the fully supervised BicycleGAN, and significantly betterthan all unsupervised baselines. In Fig. 5, we show more example results on edges↔ shoes/handbags. Our model produce diverse translations in both directions.

We proceed to perform experiments on the animal image translation dataset.As shown in Fig. 6, our model successfully translate one kind of animal to an-other. Given an input image, the translation outputs cover multiple modes, i.e.,multiple fine-grained animal categories in the target domain. The shape of ananimal has undergone significant transformations, but the pose is overall pre-served. As shown in Table 2, our model obtains higher scores than all baselinemethods according to both CIS and IS. In particular, the baselines all obtaina very low CIS, indicating their failure to generate multimodal outputs from


Table 2. Quantitative evaluation on animal image translation. This dataset contains 3domains. We perform bidirectional translation for each domain pair, resulting in 6translation tasks. We use CIS and IS to measure the performance on each task.

CycleGANCycleGAN*with noise

UNIT MUNIT

CIS IS CIS IS CIS IS CIS IS

house cats → big cats 0.078 0.795 0.034 0.701 0.096 0.666 0.911 0.923

big cats → house cats 0.109 0.887 0.124 0.848 0.164 0.817 0.956 0.954

house cats → dogs 0.044 0.895 0.070 0.901 0.045 0.827 1.231 1.255

dogs → house cats 0.121 0.921 0.137 0.978 0.193 0.982 1.035 1.034

big cats → dogs 0.058 0.762 0.019 0.589 0.094 0.910 1.205 1.233

dogs → big cats 0.047 0.620 0.022 0.558 0.096 0.754 0.897 0.901

Average 0.076 0.813 0.068 0.762 0.115 0.826 1.039 1.050

a given input. As the IS has been shown to correlate well to image generationquality [34], the higher IS of our method suggests that it also generates imagesof high quality than the baseline approaches.

Fig. 7 demonstrates multimodal image translations on street scene datasets.Our model is able to generate SYNTHIA images with diverse renderings (e.g.,rainy, snowy, sunset) from a given Cityscape image, and generate Cityscapeimages with different lighting, shadow, and road textures from a given SYNTHIAimage. Similarly, it generates winter images with different amount of snow froma given summer image, and summer images with different amount of leafs froma given winter image. Fig. 8 shows example results of summer↔ winter transferon the high-resolution Yosemite dataset. Our algorithm can not only change theseason but also generate output images with different lighting conditions.

Example-guided Image Translation. Our method provides users more con-trol on the image translation outputs due to the disentangled representation ofcontent and style. Instead of sampling a style code from the prior distribution,we can use the style code of a reference image in the target domain to generatethe desired translation output. Specifically, given a content image x1 ∈ X1 anda style image x2 ∈ X2, our model produce an image x1→2 that recombines thecontent of the former and the style latter by x1→2 = G2(Ec

1(x1), Es2(x2)). Some

example results are shown in Fig. 9. In Fig. 10, we compare out method withclassical style transfer algorithms including Gatys et al. [5], Chen et al. [83],AdaIN [52], and WCT [53]. Our method produces results that are significantlymore faithful and realistic, since our method learns the distribution of targetdomain images using GANs.

6 Conclusions

We presented a framework for multimodal unsupervised image-to-image transla-tion. Our model achieves quality and diversity superior to existing unsupervised



(a) Cityscape → SYNTHIA

(b) SYNTHIA → Cityscape

(c) summer → winter

(d) winter → summer

Fig. 7. Example results on street scene translations.


(a) Yosemite summer → winter

(b) Yosemite winter → summer

Fig. 8. Example results on Yosemite summer ↔ winter (HD resolution).

methods and comparable to state-of-the-art supervised approach. Future workincludes extending this framework to other domains, such as videos and text.


Content

Style

Content

Style

(b) edges → shoes (b) big cats → house cats

Fig. 9. Example-guided image translation. Each row has the same content while eachcolumn has the same style.

Input Style Ours Gatys et al. Chen et al. AdaIN WCT

Fig. 10. Comparison with existing style transfer methods.


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Appendix

A Proofs

Proposition 1. Suppose there exists E∗1 , E∗2 , G∗1, G∗2 such that: 1) E∗1 = (G∗1)−1

and E∗2 = (G∗2)−1, and 2) p(x1→2) = p(x2) and p(x2→1) = p(x1). Then E∗1 , E∗2 ,G∗1, G∗2 minimizes L(E1, E2, G1, G2) = max

D1,D2

L(E1, E2, G1, G2, D1, D2) (Eq. (5)).

Proof.

L(E1, E2, G1, G2) = maxD1,D2

L(E1, E2, G1, G2, D1, D2) = maxD1

Lx1

GAN + maxD2

Lx2

GAN

+λx(Lx1recon + Lx2

recon) + λc(Lc1recon + Lc2

recon) + λs(Ls1recon + Ls2

recon)

As shown in Goodfellow et al. [27], maxD2

Lx2

GAN = 2 · JSD(p(x2)|p(x1→2))− log 4

which has a global minimum when p(x2) = p(x1→2). Also, the bidirectional


reconstruction loss terms are minimized when Ei inverts Gi. Thus the total lossis minimized under the two stated conditions. Below, we assume the networkshave sufficient capacity and the optimality is reachable as in prior works [27, 43].That is E1 → E∗1 , E2 → E∗2 , G1 → G∗1, and G2 → G∗2.

Proposition 2. When optimality is reached, we have:

p(c1) = p(c2), p(s1) = q(s1), p(s2) = q(s2)

Proof. Let z1 denote the latent code, which is the concatenation of c1 and s1.We denote the encoded latent distribution by pE(z1), which is defined by z1 =E1(x1) and x1 sampled from the data distribution p(x1). We denote the latentdistribution at generation time by p(z1), which is obtained by s1 ∼ q(s1) andc1 ∼ p(c2). The generated image distribution pG(x1) = p(x2→1) is defined byx1 = G1(z1) and z1 sampled from p(z1). According to the change of variableformula for probability density functions:

pG(x1) = |∂G−11 (x1)

∂x1|p(G−11 (x1))

pE(z1) = |∂E−11 (z1)

∂z1|p(E−11 (z1))

According to Proposition 1, we have pG(x1) = p(x1) and E1 = G−11 whenoptimality is reached. Thus:

pE(z1) = |∂E−11 (z1)

∂z1|p(E−11 (z1))

= |∂E−11 (z1)

∂z1|pG(E−11 (z1))

= |∂E−11 (z1)

∂z1||∂G

−11 (E−11 (z1))

∂E−11 (z1)|p(G−11 (E−11 (z1)))

= |∂E−11 (z1)

∂z1||∂G

−11 (G1(z1))

∂E−11 (z1)|p(G−11 (G1(z1)))

= |∂E−11 (z1)

∂z1|| ∂z1

∂E−11 (z1)|p(G−11 (G1(z1)))

= p(z1)

Similarly we have pE(z2) = p(z2), which together prove the original proposition.From another perspective, we note that Lc2

recon,Ls1recon,Lx1

GAN coincide with theobjective of a WAE [39] or AAE [84] in the latent space, which pushes theencoded latent distribution towards the latent distribution at generation time.

Proposition 3. When optimality is reached, we have p(x1, x1→2) = p(x2→1, x2).

Proof. For the ease of notation we denote the joint distribution p(x1, x1→2)by p1→2(x1, x2) and p(x2→1, x2) by p2→1(x1, x2). Both densities are zero when


Ec1(x1) 6= Ec

2(x2). When Ec1(x1) = Ec

2(x2), we also have:

p1→2(x1, x2) = pG(x2|Ec1(x1))p(x1)

= |∂Es2(x2)

x2|q(Es

2(x2))p(x1)

= p(x2|Ec1(x1))pG(x1)

= p2→1(x1, x2)

Proposition 4. Denote h1 = (x1, s2) ∈ H1 and h2 = (x2, s1) ∈ H2. h1, h2 arepoints in the joint spaces of image and style. Our model defines a deterministicmapping F1→2 from H1 to H2 (and vice versa) by F1→2(h1) = F1→2(x1, s2) ,(G2(Ec

1(x1), s2), Es1(x1)). When optimality is achieved, we have F1→2 = F−12→1.

Proof.

F2→1(F1→2(x1, s2)) , F2→1(G2(Ec1(x1), s2), Es

1(x1)) (9)

, (G1(Ec2(G2(Ec

1(x1), s2)), Es1(x1)), Es

2(G2(Ec1(x1), s2)))

(10)

= (G1(Ec2(G2(Ec

1(x1), s2)), Es1(x1)), s2) (11)

= (G1(Ec1(x1), Es

1(x1)), s2) (12)

= (x1, s2) (13)

And we can prove F1→2(F2→1(x2, s1)) = (x2, s1) in a similar manner. To be morespecific, (3) is implied by the style reconstruction loss Ls

recon, (4) is implied by thecontent reconstruction loss Lc

recon, and (5) is implied by the image reconstructionloss Lx

recon. As a result, style-augmented cycle consistency is implicitly impliedby the proposed bidirectional reconstruction loss.

Proposition 5. (Cycle consistency implies deterministic translations).Let p(x1) and p(x2) denote the data distributions. pG(x1|x2) and pG(x2|x1) aretwo conditionals defined by generators. Given 1) matched marginals: p(x1) =∫pG(x1|x2)p(x2) dx2, p(x1) =

∫pG(x2|x1)p(x1) dx1, and 2) cycle consistency:

Ex2∼pG(x2|x∗1)[pG(x1|x2)] = δ(x1 − x∗1), Ex1∼pG(x1|x∗2)[pG(x2|x1)]= δ(x2 − x∗2) forevery x∗1 ∈ X1, x

∗2 ∈ X2, then pG(x1|x2) and pG(x2|x1) collapse to deterministic

delta functions.

Proof. Let x∗1 be a sample from p(x1). x′2, x′′2 are two samples from pG(x2|x∗1).Due to cycle consistency in X1 → X2 → X1, we have pG(x1|x′2) = pG(x1|x′′2) =δ(x1 − x∗1). Also, x′2 ∈ X2 and x′′2 ∈ X2 because of matched marginals. Dueto cycle consistency in X2 → X1 → X2, we have pG(x2|x∗1) = δ(x2 − x′2) =δ(x2 − x′′2). Thus pG(x2|x1) collapses to a delta function, similar for pG(x1|x2).This proposition shows that cycle consistency [8] is a too strong constraint formultimodal image translation.


B Training Details

B.1 Hyperparameters

We use the Adam optimizer [85] with β1 = 0.5, β2 = 0.999, and an initiallearning rate of 0.0001. The learning rate is decreased by half every 100, 000iterations. In all experiments, we use a batch size of 1 and set the loss weightsto λx = 10, λc = 1, λs = 1. We use the domain-invariant perceptual loss withweight 1 in the street scene and Yosemite datasets. We choose the dimension ofthe style code to be 8 across all datasets. Random mirroring is applied duringtraining.

B.2 Network Architectures

Let c7s1-k denote a 7 × 7 convolutional block with k filters and stride 1. dkdenotes a 4 × 4 convolutional block with k filters and stride 2. Rk denotes aresidual block that contains two 3 × 3 convolutional blocks. uk denotes a 2×nearest-neighbor upsampling layer followed by a 5× 5 convolutional block withk filters and stride 1. GAP denotes a global average pooling layer. fck denotes afully connected layer with k filters. We apply Instance Normalization (IN) [69]to the content encoder and Adaptive Instance Normalization (AdaIN) [52] tothe decoder. We use ReLU activations in the generator and Leaky ReLU withslope 0.2 in the discriminator. We use multi-scale discriminators with 3 scales.

– Generator architecture• Content encoder: c7s1-64, d128, d256, R256, R256, R256, R256

• Style encoder: c7s1-64, d128, d256, d256, d256, GAP, fc8

• Decoder: R256, R256, R256, R256, u128, u64, c7s1-3

– Discriminator architecture: d64, d128, d256, d512

Multimodal Unsupervised Image-to-Image Translation · Translation (MUNIT) framework. We assume that...

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