Unpaired Diffusion Translation

• Unpaired Diffusion Translation is a framework that employs diffusion-type models, including score-based SDEs and latent diffusion, to bridge unaligned source and target domains.
• It integrates optimal transport, conditional score learning, and implicit bridge methods to enforce structure and semantic consistency during the translation process.
• Recent advances focus on efficiency with distilled one-step translators and robust coupling mechanisms, enhancing applications in medical imaging, remote sensing, and more.

Unpaired diffusion translation denotes a family of methods that learn mappings between source and target domains from unpaired datasets, using diffusion-type generative models, score-based SDEs, probability-flow ODEs, latent diffusion models, or diffusion bridges. In its canonical form, one observes only marginal samples from two domains, such as $\mathcal{S}_A=\{x^{a}\}\sim p_A$ and $\mathcal{S}_B=\{x^{b}\}\sim p_B$, with no one-to-one correspondences, and seeks a mapping that places outputs on the target-domain manifold while preserving source-domain content or geometry (Lee et al., 19 Mar 2025). Because only marginals are given, the problem is inherently under-constrained: modality translation can be viewed as selecting a coupling $p(x,y)$ from the infinite set $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$, so additional inductive bias is required to determine which cross-domain correspondence is realized (Kosman et al., 3 May 2026).

1. Formal problem and sources of ambiguity

Across the literature, the unpaired setting is written as two independent datasets from distinct domains, with no aligned pairs. In surgery, for example, simulated images $x^{\text{sim}}$ and real images $x^{\text{real}}$ share rough semantic content but no one-to-one spatial correspondence, and paired translation methods are therefore not applicable (Venkatesh et al., 2024). A closely related abstraction appears in bidirectional unpaired translation, where one model must support $A\to B$ and $B\to A$ using only $\mathcal{S}_A$ and $\mathcal{S}_B$ (Lee et al., 19 Mar 2025).

This lack of pairing makes the task non-identifiable. A distribution-level match $\mathcal{S}_B=\{x^{b}\}\sim p_B$0 does not by itself determine which source structures should be preserved in the translated output. OTCS makes this point explicitly by reformulating conditional score-based diffusion training as an expectation over a coupling, then replacing the unavailable hard pairing with an estimated soft coupling $\mathcal{S}_B=\{x^{b}\}\sim p_B$1 derived from $\mathcal{S}_B=\{x^{b}\}\sim p_B$2-regularized optimal transport (Gu et al., 2023). Structured Diffusion Bridges generalize the same idea: when only marginals are observed, diffusion translation must be understood as choosing one admissible coupling from a large feasible set, and the quality of a method depends on the structural assumptions used to narrow that set (Kosman et al., 3 May 2026).

Different application domains instantiate the same formal difficulty. Histopathology FS$\mathcal{S}_B=\{x^{b}\}\sim p_B$3FFPE translation uses different slides and tissue levels with no registration (Ho et al., 2024). SAR-to-optical aircraft translation uses different sensors and times, with only class labels and keypoints rather than paired chips (You et al., 25 Mar 2025). EEG$\mathcal{S}_B=\{x^{b}\}\sim p_B$4fMEG translation is unpaired because simultaneous fetal EEG and fMEG are essentially infeasible (Brebion et al., 16 Jul 2025). Fluid-dynamics super-resolution likewise treats low-fidelity low-resolution and high-fidelity low-resolution simulations as separate distributions without sample-wise alignment (Xu et al., 7 Apr 2025).

2. Dynamical formulations: diffusion, PF-ODEs, and bridges

A large portion of the field inherits the score-based diffusion formulation. In one common notation, the forward noising process is

$\mathcal{S}_B=\{x^{b}\}\sim p_B$5

and sampling is performed by integrating the probability-flow ODE

$\mathcal{S}_B=\{x^{b}\}\sim p_B$6

with the score approximated by a neural denoiser or noise-prediction network (Venkatesh et al., 2024). This makes diffusion translation a problem of controlling or reinterpreting the reverse trajectory so that it lands in a different domain while retaining source information.

One influential interpretation is the implicit bridge. DDIB trains one diffusion model per domain, independently, and performs translation by solving the source PF-ODE forward from data to Gaussian noise and then the target PF-ODE backward from the same latent to data. In schematic form,

$\mathcal{S}_B=\{x^{b}\}\sim p_B$7

which yields a deterministic, cycle-consistent mapping up to discretization error (Su et al., 2022). The EEG–fMEG work uses the same dual-bridge principle for 1D biomedical signals, with EDM-based PF-ODEs and improved numerical integration (Brebion et al., 16 Jul 2025).

A second viewpoint comes from Schrödinger bridges. UNSB formulates unpaired image-to-image translation as learning a stochastic process $\mathcal{S}_B=\{x^{b}\}\sim p_B$8 that minimizes $\mathcal{S}_B=\{x^{b}\}\sim p_B$9 subject to endpoint marginals $p(x,y)$0 and $p(x,y)$1, thereby replacing the Gaussian endpoint of standard diffusion with an arbitrary target-domain marginal (Kim et al., 2023). In this perspective, unpaired translation becomes an entropic optimal-transport problem between two empirical image distributions rather than a data-to-noise generative model.

A third formulation is conditional score learning with soft couplings. OTCS estimates a compatibility function

$p(x,y)$2

from unsupervised or semi-supervised optimal transport, then uses $p(x,y)$3 to replace missing pair information in conditional denoising score matching (Gu et al., 2023). This yields a conditional diffusion model trained from unpaired or partially paired data rather than a target-only generator edited at inference time.

3. Main design paradigms

Several recurrent design patterns organize the literature.

Paradigm	Core mechanism	Representative papers
Target-domain editing	Learn the target distribution only, inject the source at inference through SDEdit-like editing or guidance	SurgicaL-CD (Venkatesh et al., 2024), Contrastive-SDE (Kotyada et al., 4 Oct 2025)
Dual or implicit bridges	Encode source to a shared Gaussian or bridge latent, then decode with the target model	DDIB (Su et al., 2022), EEG–fMEG bridges (Brebion et al., 16 Jul 2025), fluid dynamics EDDIB (Xu et al., 7 Apr 2025)
Coupling- or semantic-guided conditional models	Estimate soft pairings or shared semantics through OT, embeddings, keypoints, or self-supervised encoders	OTCS (Gu et al., 2023), F2FLDM (Ho et al., 2024), KeypointDiff (You et al., 25 Mar 2025), SSB (Liu et al., 18 Feb 2026)
Distilled translators	Compress multi-step diffusion or bridge dynamics into few-step or one-step generators	R-DMD (Rakitin et al., 2024), SurgicaL-CD (Venkatesh et al., 2024), IBCD (Lee et al., 19 Mar 2025)

Target-domain editing methods decouple learning the target manifold from translation itself. SurgicaL-CD fine-tunes Stable Diffusion on real surgical images, distills it to a latent consistency model, and then applies SDEdit to noised simulated images, optionally with OT color transfer and ControlNet, so the source image is used only at inference (Venkatesh et al., 2024). Contrastive-SDE follows a related philosophy but guides a pretrained target-domain SDE with a time-dependent contrastive objective that preserves domain-invariant features (Kotyada et al., 4 Oct 2025).

Bridge-based methods instead define the translation path itself as the primary object. DDIB and its 1D and fluid-dynamics descendants use shared Gaussian endpoints and concatenated PF-ODEs (Su et al., 2022, Brebion et al., 16 Jul 2025, Xu et al., 7 Apr 2025). UNSB uses an adversarially trained Schrödinger bridge between arbitrary endpoint distributions (Kim et al., 2023). Structured Diffusion Bridges extend the bridge view by adding marginal matching and cycle constraints so that the same framework remains applicable in unpaired, semi-paired, and paired regimes (Kosman et al., 3 May 2026).

Coupling-guided and semantic-latent methods introduce an explicit intermediate representation. OTCS uses transport couplings $p(x,y)$4 (Gu et al., 2023). F2FLDM conditions SDXL on histopathology embeddings and adds an embedding translator $p(x,y)$5 trained with WGAN-GP in cycle fashion to map FS embeddings into FFPE-like embeddings (Ho et al., 2024). KeypointDiff uses aircraft keypoints and angle information as structured conditions (You et al., 25 Mar 2025). SSB uses self-supervised visual encoders to build a semantic latent space that is invariant to appearance changes but retains geometry (Liu et al., 18 Feb 2026).

4. Conditioning and structure preservation

Because unpaired translation is under-constrained, most successful systems add explicit mechanisms for preserving source structure. In SurgicaL-CD, content preservation is implicit in SDEdit—starting from a noised version of the source image keeps the reverse trajectory close to the original geometry—and is strengthened by ControlNet with soft edges or depth; ablations show that without ControlNet, edges and structures are smoothed or distorted (Venkatesh et al., 2024). The same system also uses OT color transfer as a lightweight pre-alignment before diffusion, which reduces the source–target color gap (Venkatesh et al., 2024).

Histopathology translation in F2FLDM relies on a different structural decomposition. FS and FFPE images are encoded into a shared SDXL latent space, while a histopathology-pretrained encoder produces embeddings $p(x,y)$6. A separate embedding translator maps $p(x,y)$7 to $p(x,y)$8, and the inference-time condition is blended as

$p(x,y)$9

with $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$0 reported as the best trade-off between FFPE style and FS identity (Ho et al., 2024). Translation is then implemented by DDIM inversion of the FS image and reverse denoising under FFPE text and embedding conditions.

KeypointDiff makes structure explicit. Aircraft nose and tail keypoints define a principal axis and azimuth angle, which are injected through a Class-Angle Guidance Module using FiLM and self-attention. The method also constructs pseudo-pairs by selecting an optical chip of the same class and rotating it to align its nose–tail direction with the SAR sample, thereby providing structural supervision without true pairing (You et al., 25 Mar 2025).

Contrastive-SDE imposes preservation in feature space. A time-dependent SimCLR encoder is trained with an image and its low-pass filtered version as a positive pair, so the learned representation emphasizes domain-invariant content. During reverse diffusion, the guidance term

$$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$1

is differentiated with respect to the current sample, steering generation toward outputs whose contrastive features match those of the source image (Kotyada et al., 4 Oct 2025). SSB pushes the same idea further by using self-supervised visual encoders to define a semantic latent that is invariant to appearance but captures geometry, and then conditioning diffusion bridges on that latent (Liu et al., 18 Feb 2026).

5. Distillation, efficiency, and one-step translation

A persistent practical issue is that iterative diffusion and bridge sampling can require tens to hundreds of function evaluations. Several recent methods therefore compress multi-step dynamics into few-step or one-step translators.

SurgicaL-CD distills a fine-tuned Stable Diffusion model into a latent consistency model and reports 1, 2, or 4 inference steps. Its inference time is $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$2–$$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$3 s per image for 1–4 steps, compared with $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$4–$$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$5 s for 20-step SDEdit baselines, corresponding to roughly $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$6 speedup while retaining strong semantic consistency and downstream segmentation utility (Venkatesh et al., 2024).

R-DMD takes a different route. It adapts Distribution Matching Distillation to unpaired image-to-image translation by training a one-step generator $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$7 whose noised outputs match the target diffusion model, while a regularizer $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$8 selects low-cost mappings among all target-distribution-matching solutions (Rakitin et al., 2024). The paper shows that, for quadratic cost and $$\mathcal{P}=\{p(x,y)\mid p(x)=p_{\mathcal X},\,p(y)=p_{\mathcal Y}\}$$9, the optimal map converges to the Monge optimal transport map (Rakitin et al., 2024).

IBCD extends consistency distillation from data-to-noise PF-ODEs to concatenated domain-to-domain implicit bridges. It trains a single conditional student $x^{\text{sim}}$0 over signed timesteps that span the whole $x^{\text{sim}}$1 path, adds a distribution-matching regularizer and adaptive weighting based on distillation difficulty, and performs single-step bidirectional translation at inference. On Cat$x^{\text{sim}}$2Dog, IBCD reports about $x^{\text{sim}}$3 s/image at 1 NFE, versus about $x^{\text{sim}}$4 s/image and 160 NFEs for the DDIB teacher, and 6–26 s/image for EGSDE, SDEdit, and CycleDiffusion baselines (Lee et al., 19 Mar 2025).

Efficiency also depends on numerical integration, not only on distillation. In EEG–fMEG translation, replacing DDIB’s DDIM-style first-order solver with EDM plus Heun’s method reduces NFE from 500 to 118 while substantially improving reconstruction fidelity in both time and frequency domains (Brebion et al., 16 Jul 2025). A related data-efficiency argument appears in DRDD, where the stochastic noise-diffusion stage is trained exclusively on abundant, unpaired target-domain images and the semantic residual mapping is learned separately in the fixed-noise domain, thereby improving performance under limited paired data (Lin et al., 31 May 2026).

6. Applications, evaluation, and open problems

Unpaired diffusion translation now spans a broad set of domains. Surgical image generation translates simulated laparoscopic scenes into realistic endoscopic images (Venkatesh et al., 2024). Histopathology translates frozen sections into FFPE-like slides (Ho et al., 2024). Visible–infrared person image translation has been proposed for single-modality-labeled VI-ReID, with a diffusion model reported to outperform existing diffusion and GAN models (Huang et al., 2023). Object-level SAR-to-optical translation uses keypoints for aircraft geometry (You et al., 25 Mar 2025). Biomedical signal translation maps spontaneous premature neonatal EEG and fetal MEG bursts through dual diffusion bridges (Brebion et al., 16 Jul 2025). Fluid-dynamics super-resolution uses unpaired low-resolution domain translation before cascaded spatial refinement (Xu et al., 7 Apr 2025). The terminology also appears in multilingual text diffusion, where multinomial diffusion is used for zero-shot translation between language pairs unseen during training, such as DE$x^{\text{sim}}$5FR and FR$x^{\text{sim}}$6DE (Nachmani et al., 2021).

The evaluation culture is correspondingly heterogeneous. Surgical translation uses CFID, CMMD, Density & Coverage, LPIPS, segmentation Dice, and downstream segmentation gains (Venkatesh et al., 2024). Histopathology emphasizes kidney subtype classification AUC, accuracy, and CaseFD in pathology feature spaces (Ho et al., 2024). KeypointDiff measures FID, overall accuracy of a pretrained detector, and angle error (You et al., 25 Mar 2025). EEG–fMEG translation evaluates time-domain MSE, MSE/MAV ratio, and power spectral density across Delta, Theta, Alpha, and lower Beta bands (Brebion et al., 16 Jul 2025). Fluid-dynamics translation uses energy spectra, MELR, TVD, RMSE, MMD, and $x^{\text{sim}}$7 (Xu et al., 7 Apr 2025). This strongly suggests that generic image realism metrics alone are insufficient for unpaired diffusion translation; domain-specific fidelity and downstream-task criteria are often decisive.

Several unresolved issues recur. Structured Diffusion Bridges state the problem most sharply: modality translation remains non-identifiable from marginals alone, and even a valid bridge can implement an undesirable coupling unless constrained by additional structure (Kosman et al., 3 May 2026). The same paper notes that marginal matching can ignore the conditioning endpoint and behave like unconditional diffusion, while endpoint cycle consistency alone does not constrain intermediate trajectories adequately; trajectory-level cycle losses improve this but do not eliminate ambiguity (Kosman et al., 3 May 2026). Across the literature, there is also no consensus on optimization principle. UNSB solves unpaired translation through a sequence of adversarial learning problems that approximate a Schrödinger bridge (Kim et al., 2023), whereas IBCD emphasizes single-step bidirectional translation without adversarial loss (Lee et al., 19 Mar 2025). This suggests a live methodological divide between adversarially regularized bridges, target-only editing, OT-guided conditional models, and distilled one-step generators.

A plausible synthesis is that unpaired diffusion translation has become less a single algorithm than a design space. Some methods learn the target manifold and perform translation as editing; others learn an explicit bridge between marginals; others estimate couplings or semantic latents that stand in for missing pairs; and newer work increasingly compresses these dynamics into one-step or few-step translators. What unifies them is the central claim that diffusion-type dynamics can model high-fidelity target distributions while providing enough controllability to preserve cross-domain structure even when direct supervision is absent.