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 → 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 D(⋅,cB) and its one-step approximation Et[D^(⋅,cB)] for A → B translation, with g selected as a logarithm.
Method
NFE ↓
FID ↓
PSNR ↑
SSIM ↑
Density ↑
Coverage ↑
Cat → 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 † 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 → 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 ).
Figure 5: Brain MRI contrast translation (BraTS2021, T1 → T2), with the paired T2 reference. More in App. G.13 .
Method
Params [M]
NFE ↓
Time [ s/img ] ↓
Rel. ↓
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 ]
≫1
≫1
30.32
2526.67
DDIB (Teacher) [ 47 ]
32.95
160
1.45
120.83
Table 3: Inference cost on the Cat → 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 ↓
PSNR ↑
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 → 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. cskip,cout, and cin are shown for c=cB (the translation direction is XA→XB ).
Model
Cat ↔ Dog
Wild ↔ Dog
Male ↔ Female
Configuration
IBCD
IBCD †
IBCD
IBCD †
IBCD
IBCD †
λDMCD
1
0.18
0.2
0.2
0.02
0.02
λcycle
0.03
0.003
0.001
0.0003
0.00001
0.00003
g(⋅)
1
min(0,log(⋅)+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 → 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 → 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 → 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)
sϕ
32.95
PF-ODE targets, real score
✗
frozen
✓
✓
Student
Gθ
32.95
the deployed translator
✓
gradient step on Ltotal , ζθ= 4e-5
✓
✓
CD target
Gθ−
32.95
target branch of LIBCD
✗
EMA of θ , μ=0.95
✓
✓
Inference copy
GθEMA
32.95
evaluation only
✗
EMA of θ , μ=0.9999432…
✓
✓
Fake score network
sψ
32.95
student-distribution score in LDMCD
✓
DSM on student outputs, ζψ= 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 θ and ψ receive gradients and carry optimizer state; θ− and θEMA are exponential moving averages of θ and are never differentiated; ϕ 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 → Dog
Wild → Dog
Male → Female
Method
NFE
Realism ↑
Faithfulness ↑
Preference ↑
LPIPS ↓
CLIP ↑
LPIPS ↓
CLIP ↑
LPIPS ↓
CLIP ↑
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 †
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 † ).
Figure S3 : Ablation study results on Cat → 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 ( λDMCD , λcycle ) for the Male → Female task. In (a) λcycle was set to 0, and in (b) λDMCD was set to 0.10. Distillation difficulty adaptive weighting was not applied.
Cat → Dog
Dog → Cat
Distance
FID ↓
PSNR ↑
SSIM ↑
FID ↓
PSNR ↑
SSIM ↑
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 Et[D^(⋅,cFEMALE)] and the translations performed in the Male → Female task.
Figure S6 : Visualization of the training loss curve highlighting the stability of our framework on the Cat → 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 ↓
Time [ s/img ] ↓
Relative Time ↓
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 ↓
FID ↓
PSNR ↑
SSIM ↑
Density ↑
Coverage ↑
Dog → 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 † (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 ↑
SSIM ↑
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.
Bidirectional unpaired image translation must preserve source-specific structure while learning coherent transformations in both directions without paired supervision. Existing methods typically employ two direction-specific generators or train separate one-way models. Even when linked by cycle consistency, such models constrain only the round-trip endpoint reconstruction, without requiring the two directions to obey a common local transformation rule. We propose UniCycleFlow, a rectified-flow framework that represents bidirectional translation as forward and reverse integration of a single time-conditioned velocity field. This formulation organizes both directions within the same continuous dynamics, rather than coupling otherwise separate endpoint mappings. A key challenge is that unpaired data provide no meaningful source--target coupling from which rectified-flow trajectories can be constructed. UniCycleFlow addresses this challenge by learning deterministic source-conditioned endpoints whose marginal distributions are adversarially matched to the opposite domains. The resulting paths are regularized by stop-gradient self-flow matching for intermediate velocity supervision, discrete cycle closure for forward--reverse consistency, and representation path-velocity regularization for controlling localized feature changes along the trajectory. Across ten translation directions, UniCycleFlow achieves the lowest FID on 7 of 10 tasks using a single Euler evaluation and obtains the best average FID of 55.1.
Xianhao Zhou, Jianghao Wu, Shaoting Zhang +1
School of Mechanical and Electrical Engineering, University of Electronic Science and Technology of China, Chengdu, China · Faculty of Information Technology, Monash University, Melbourne, Australia · Shanghai Artificial Intelligence Laboratory, Shanghai, China
Modality translation is inherently under-constrained, as multiple cross-modal mappings may yield the same marginals. Recent work has shown that diffusion bridges are effective for this task. However, most existing approaches rely on fully paired datasets, thereby imposing a single data-driven constraint. We propose a diffusion-bridge framework that characterizes the space of admissible solutions and restricts it via alignment constraints, treating paired supervision as an optional heuristic rather than a prerequisite. We validate our method on synthetic and real modality translation benchmarks across unpaired, semi-paired, and paired regimes, showing consistent performance across supervision levels. Notably, it achieves near fully-paired quality with a substantial relaxation in pairing requirements, and remaining applicable in the unpaired regime. These results highlight diffusion bridges as a flexible foundation for modality translation beyond fully paired data.
Adversarial diffusion and diffusion-inversion methods have advanced unpaired image-to-image translation, but each faces key limitations. Adversarial approaches require target-domain adversarial loss during training, which can limit generalization to unseen data, while diffusion-inversion methods often produce low-fidelity translations due to imperfect inversion into noise-latent representations. In this work, we propose the Self-Supervised Semantic Bridge (SSB), a versatile framework that integrates external semantic priors into diffusion bridge models to enable spatially faithful translation without cross-domain supervision. Our key idea is to leverage self-supervised visual encoders to learn representations that are invariant to appearance changes but capture geometric structure, forming a shared latent space that conditions the diffusion bridges. Extensive experiments show that SSB outperforms strong prior methods for challenging medical image synthesis in both in-domain and out-of-domain settings, and extends easily to high-quality text-guided editing.
Jiaming Liu, Felix Petersen, Yunhe Gao +6
Stanford University · LLNL · Johns Hopkins University