Single-Step Bidirectional Unpaired Image Translation Using Implicit Bridge Consistency Distillation

Suhyeon Lee; Kwanyoung Kim; Jong Chul Ye

cs.CVMar 19, 2025

Single-Step Bidirectional Unpaired Image Translation Using Implicit Bridge Consistency Distillation

Authors: Suhyeon Lee, Kwanyoung Kim, Jong Chul Ye

Organizations: Kim Jae Chul Graduate School of AI, KAIST · Samsung Research

Abstract

Unpaired image-to-image translation has seen significant progress since the introduction of CycleGAN. However, methods based on diffusion models or Schrödinger bridges have yet to be widely adopted in real-world applications due to their iterative sampling nature. To address this challenge, we propose Implicit Bridge Consistency Distillation (IBCD), which enables single-step bidirectional unpaired translation without using adversarial loss. IBCD reformulates consistency distillation by using a diffusion implicit bridge model that connects PF-ODE trajectories between distributions, parametrized on a signed time axis whose sign selects the target domain, so that one network translates in both directions in a single step. Additionally, we introduce two key improvements: 1) distribution matching for consistency distillation and 2) adaptive weighting method based on distillation difficulty. Experimental results demonstrate that IBCD achieves state-of-the-art performance on benchmark datasets in a single generation step, and that it extends to brain MRI contrast translation.

Figures & tables

Figure 1: Peak signal-to-noise ratio (PSNR) and Fréchet inception distance (FID) trade-off comparison with baselines on the Cat

\rightarrow

Dog task, where PSNR is measured against the source image (Sec. 4.2 ). Marker size represents the number of NFE.

Figure 2: (a) IBCD performs single-step bi-directional translation using a distillation framework that reformulates consistency distillation with a diffusion implicit bridge and introduces regularizers. (b) The IBCD framework bridges two distributions by connecting the PF-ODE paths of two pre-trained diffusion models through bidirectionally extended consistency distillation. To mitigate distillation errors, we introduce distribution matching for consistency distillation and a cycle translation loss.

Figure 3: (a) Bidirectional translation results on a toy dataset, showing the contributions of each component. The boxes mark the inset region, the same portion of the outer branch of the target Swiss roll in every panel; the dotted curve is that branch’s inner boundary, traced on the ground-truth Domain B samples. (b) Visualization of distillation difficulty $\mathcal{D}(\cdot,c_{\text{B}})$ and its one-step approximation $\mathbb{E}_{t}[\hat{\mathcal{D}}(\cdot,c_{\text{B}})]$ for A $\rightarrow$ B translation, with $g$ selected as a logarithm.

Method	NFE $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	Density $\uparrow$	Coverage $\uparrow$
Cat $\rightarrow$ Dog
StarGAN v2 [ 9 ]	1	54.88	10.63	0.270	-	-
CUT [ 35 ]	1	76.21	17.48	0.601	0.971	0.696
NOT ∗ [ 27 ]	1	161.54	15.12	0.566	0.531	0.072
DSBM ∗ [ 43 ]	100	100.08	21.24	0.532	0.750	0.396
UNSB ∗ [ 24 ]	5	68.59	17.65	0.587	1.045	0.706

Table 1: Quantitative comparison of unpaired image-to-image translation tasks . Most results are from the EGSDE paper, except those marked with *, which are obtained by training the model on our dataset using the default configuration, and the Density-Coverage metric [ 32 ] . Marker

\dagger

marks the same network at a hyperparameter configuration that prioritizes realism over faithfulness. PSNR/SSIM are source -referenced and measure similarity to the source, not fidelity.

Figure 4: Qualitative comparison of unpaired image-to-image translation tasks (Cat $\rightarrow$ Dog) . Compared to other baselines, our model achieves more realistic and source-faithful translations in a single step. The numbers in parentheses represent inference NFE. The teacher is omitted for space (App. G ); sources are a fixed-seed draw, not a curated one (App. G.11 ).

	vs. ground-truth T2
Method	PSNR $\uparrow$	SSIM $\uparrow$
SDEdit	29.85	0.849
EGSDE	23.34	0.842
CycleDiffusion	30.52	0.825
GPT-Image-1 (Foundation)	No valid translation
DDIB ∗ (Teacher)	30.24	0.825

Table 2: Brain MRI contrast translation (BraTS2021 [ 2 ] , T1

\rightarrow

T2), scored against paired ground truth. Setup in App. G.13 .

Figure 5: Brain MRI contrast translation (BraTS2021, T1 $\rightarrow$ T2), with the paired T2 reference. More in App. G.13 .

Method	Params [M]	NFE $\downarrow$	Time [ $s/img$ ] $\downarrow$	Rel. $\downarrow$
CUT [ 35 ]	11.39	1	0.0070	0.58
UNSB [ 24 ]	14.69	5	0.077	6.42
EGSDE [ 57 ]	147.14	1000	15.89	1324.16
CycleDiffusion [ 54 ]	187.12	1000(+100)	26.03	2169.17
GPT-Image-1 [ 33 ]	$\gg 1$	$\gg 1$	30.32	2526.67
DDIB (Teacher) [ 47 ]	32.95	160	1.45	120.83

Table 3: Inference cost on the Cat

\rightarrow

Dog task , on a single NVIDIA RTX 4090 at batch size 1 (except GPT-Image-1). One representative method per family; the full 15-row table is in App. G .

Component	FID $\downarrow$	PSNR $\uparrow$
		vs. teacher output	vs. source image
IBCD loss only	48.12	18.27	19.02
+ DMCD	44.40	17.95	16.80
+ DMCD & Cycle	44.31	18.22	17.19
+ adaptive DMCD & Cycle	44.69	18.97	18.04

Table 4: Ablation on Cat

\rightarrow

Dog. Every row is the ablated model at its own lowest-FID setting , not the deployed one. PSNR is reported against the teacher’s output, which isolates distillation error, alongside the source -referenced PSNR of Tab. 1 .

Appendix figures & tables24 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1 : Extension of EDM/CD model formulation for negative $t$ in IBCD student model. $c_{\text{skip}},c_{\text{out}},$ and $c_{\text{in}}$ are shown for $c=c_{\text{B}}$ (the translation direction is ${\mathcal{X}}_{\text{A}}\rightarrow{\mathcal{X}}_{\text{B}}$ ).

Model	Cat $\leftrightarrow$ Dog		Wild $\leftrightarrow$ Dog		Male $\leftrightarrow$ Female
Configuration	IBCD	IBCD †	IBCD	IBCD †	IBCD	IBCD †
$\lambda_{\text{DMCD}}$	1	0.18	0.2	0.2	0.02	0.02
$\lambda_{\text{cycle}}$	0.03	0.003	0.001	0.0003	0.00001	0.00003
$g(\cdot)$	1	$\min(0,\log(\cdot)+10)$
transition step	200K	200K	200K	200K	500K	500K
total distillation step	210K	230K	210K	230K	510K	520K

Appendix

Table S1: Specific hyperparameters employed by different models and configurations.

Task	Prompt
Cat $\rightarrow$ Dog	Transform the image of the cat into a realistic dog, preserving the same pose, lighting, background, and overall composition. Ensure the dog appears natural and lifelike, matching the fur color, orientation, and proportions of the original cat as closely as possible. The final image should look photorealistic and faithful to the original scene, as if the dog were actually photographed in place of the cat.
Wild $\rightarrow$ Dog	Transform the image of the wild animal into a realistic dog, preserving the same pose, lighting, background, and overall composition. Ensure the dog appears natural and lifelike, matching the fur color, orientation, and proportions of the original animal as closely as possible. The final image should look photorealistic and faithful to the original scene, as if the dog were actually photographed in place of the wild animal.
Male $\rightarrow$ Female	Transform the image of the man into a realistic woman, preserving the same pose, lighting, background, and overall composition. Ensure the woman appears natural and lifelike, matching the skin tone, orientation, and proportions of the original man as closely as possible. The final image should look photorealistic and faithful to the original scene, as if the woman were actually photographed in place of the man.

Appendix

Table S2 : Prompts used in the GPT-Image-1 translation experiment for each task. These prompts were provided to the gpt-4.1-2025-04-14 model via the OpenAI API using the gpt-image-1-2025-04-23 tool. Each prompt was designed to preserve pose, lighting, background, and composition while achieving realistic domain translation.

Component	Symbol	Params [M]	Role	Gradients	Update rule	Stage 1	Stage 2
Teacher (EDM)	$s_{\phi}$	32.95	PF-ODE targets, real score	✗	frozen	✓	✓
Student	$G_{\theta}$	32.95	the deployed translator	✓	gradient step on ${\mathcal{L}}_{\text{total}}$ , $\zeta_{\theta}=$ 4e-5	✓	✓
CD target	$G_{\theta^{-}}$	32.95	target branch of ${\mathcal{L}}_{\text{IBCD}}$	✗	EMA of $\theta$ , $\mu=0.95$	✓	✓
Inference copy	$G_{\theta_{\text{EMA}}}$	32.95	evaluation only	✗	EMA of $\theta$ , $\mu=0.9999432\ldots$	✓	✓
Fake score network	$s_{\psi}$	32.95	student-distribution score in ${\mathcal{L}}_{\text{DMCD}}$	✓	DSM on student outputs, $\zeta_{\psi}=$ 1e-4	✗	✓
Weight copies resident		4 copies (131.80M parameters) in Stage 1; 5 copies (164.75M) in Stage 2

Appendix

Table S3: Components held in memory during distillation, and the phase each is needed in. All five networks share the EDM/CD architecture, so each carries the 32.95M parameters reported for IBCD in Tab. S8 . Only

\theta

and

\psi

receive gradients and carry optimizer state;

\theta^{-}

and

\theta_{\text{EMA}}

are exponential moving averages of

\theta

and are never differentiated;

\phi

is frozen for the whole run. Stage 1 is the phase before the transition step, Stage 2 the phase after it.

Figure S2 : Incorrect mapping to low-density regions due to distillation error. (a) Generation and (b) translation results using vanilla IBCD. Samples with high distillation difficulty ( i.e. , large distillation errors), which originate near the source domain decision boundary, tend to be mapped to low-probability regions in the target domain.

		User Study (1:1 win rate vs. IBCD)			Cat $\rightarrow$ Dog		Wild $\rightarrow$ Dog		Male $\rightarrow$ Female
Method	NFE	Realism $\uparrow$	Faithfulness $\uparrow$	Preference $\uparrow$	LPIPS $\downarrow$	CLIP $\uparrow$	LPIPS $\downarrow$	CLIP $\uparrow$	LPIPS $\downarrow$	CLIP $\uparrow$
ILVR	1000	0.25	0.49	0.25	0.454	72.65	0.486	67.22	-	-
SDEdit	1000	0.38	0.73	0.42	0.438	73.55	0.465	67.81	0.290	53.50
EGSDE	1000	0.37	0.28	0.43	0.433	73.98	0.467	67.34	0.284	53.12
EGSDE $\dagger$	1200	-	-	-	0.497	73.53	0.526	66.25	0.343	51.11
CycleDiffusion	1000	0.25	0.62	0.25	0.381	74.77	0.417	67.84	-	-

Appendix

Table S4 : User study and Perceptual Evaluation Results . User study 1:1 win rates: the proportion of users preferring each baseline over our model (IBCD) in pairwise comparisons. Values below 0.5 indicate that the majority preferred our model. When two versions of a model exist, they are compared against the default version (without

\dagger

Figure S3 : Ablation study results on Cat $\rightarrow$ Dog task. The DMCD loss improves the realism of the generated results compared to the vanilla IBCD. Additionally, the cycle translation loss and adaptive DMCD loss enhance source fidelity (as indicated by the arrows). These findings confirm that the components of IBCD work synergistically to achieve a better balance between realism and faithfulness.

Figure S4 : Effect of the auxiliary loss weights ( $\lambda_{\text{DMCD}}$ , $\lambda_{\text{cycle}}$ ) for the Male $\rightarrow$ Female task. In (a) $\lambda_{\text{cycle}}$ was set to 0, and in (b) $\lambda_{\text{DMCD}}$ was set to 0.10. Distillation difficulty adaptive weighting was not applied.

	Cat $\rightarrow$ Dog			Dog $\rightarrow$ Cat
Distance	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$
LPIPS	49.13	19.70	0.690	27.59	19.30	0.666
L1	58.77	19.74	0.697	37.89	19.38	0.682
L2	67.82	19.92	0.709	47.95	19.36	0.686
Pseudo-Huber	59.42	20.02	0.706	39.57	19.32	0.680

Appendix

Table S5 : Quantitative ablation study on distance functions for the IBCD loss. While different distance functions yield comparable source faithfulness, LPIPS achieves substantially better FID. Trained at a smaller resolution for 50K iterations, so the values are not comparable with Tab. 1 .

Figure S5 : Relationship between self-assessed approximate distillation difficulty $\mathbb{E}_{t}[\hat{\mathcal{D}}(\cdot,c_{\text{FEMALE}})]$ and the translations performed in the Male $\rightarrow$ Female task.

Figure S6 : Visualization of the training loss curve highlighting the stability of our framework on the Cat

\rightarrow

Dog task. The DMCD and cycle losses are introduced at the transition step, which for this task is 200K optimization steps (Tab. S1 ); the horizontal axis of the plot is the logging index of the run rather than the optimization step counter, so the switch appears at the corresponding logging index rather than at 200K. Before the switch both auxiliary losses are identically zero and the corresponding networks are not instantiated (App. F ).

Table 21

Method	Parameters [M]	NFE $\downarrow$	Time [ $s/img$ ] $\downarrow$	Relative Time $\downarrow$
StarGAN v2 [ 9 ]	64.45	1	0.0052	0.43
CUT [ 35 ]	11.39	1	0.0070	0.58
NOT [ 27 ]	9.72	1	0.0026	0.22
DSBM [ 43 ]	131.02	100	4.36	363.33
UNSB [ 24 ]	14.69	5	0.077	6.42
ASBM [ 14 ]	79.58	4	0.069	5.71

Appendix

Table S8: Quantitative comparison of model inference times and parameter sizes . Our method achieves higher translation quality with high parameter and inference-time efficiency.

Figure S7 : Example of failure cases, which are (a) incomplete translation and (b) incorrect cycle translation.

Method	NFE $\downarrow$	FID $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	Density $\uparrow$	Coverage $\uparrow$
Dog $\rightarrow$ Cat
StarGAN v2 [ 9 ]	1	37.73	16.02	0.399	1.336	0.778
CycleDiffusion [ 54 ]	1000(+100)	40.45	17.83	0.493	1.064	0.774
DDIB (Teacher) [ 47 ]	160	30.28	17.15	0.597	2.071	0.902
IBCD (Ours)	1	28.99	19.10	0.695	1.699	0.894
IBCD $\dagger$ (Ours)	1	28.41	17.40	0.653	2.112	0.920

Appendix

Table S9 : Quantitative comparison of unpaired image-to-image translation tasks (opposite & cycle translation) . The opposite-direction tasks used the same model and inference hyperparameters as the main direction task using bi-directionality.

Figure S8 : Extra qualitative comparison of unpaired image-to-image translation tasks. Compared to other baselines, our model achieves more realistic and source-faithful translations in a single step. The numbers in parentheses represent inference NFE.

Figure S9 : Qualitative comparison of unpaired image-to-image translation tasks (opposite translation) . Compared to other baselines, our model achieves more realistic and source-faithful translations in a single step. The numbers in parentheses represent inference NFE.

Figure S10 : Qualitative comparison of unpaired image-to-image translation tasks (cycle translation) . Compared to other baselines, our model achieves consistent cycle translations in a single step. The numbers in parentheses represent inference NFE.

	compared with G.T.
Method	PSNR $\uparrow$	SSIM $\uparrow$
SDEdit	29.85	0.849
EGSDE	23.34	0.842
CycleDiffusion	30.52	0.825
GPT-Image-1 (Foundation)	No valid translation
DDIB ∗ (Teacher)	30.24	0.825

Appendix

Table S10 : Quantitative comparison of unpaired MRI contrast translation tasks. PSNR/SSIM are measured against the paired ground-truth target-contrast image. Reproduced compactly as Tab. 2 of the main paper.

Figure S11 : Qualitative comparison of unpaired MRI contrast translation tasks.

Figure S12 : Limitations of foundational models in domain-specific translation.

Figure S13 : Result of the bi-directional cycle translation with a single model for the Cat $\leftrightarrow$ Dog task (IBCD † ).

Figure S14 : Result of the bi-directional cycle translation with a single model for the Wild $\leftrightarrow$ Dog task (IBCD † ).

Figure S15 : Result of the bi-directional cycle translation with a single model for the Male $\leftrightarrow$ Female task (IBCD † ).

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