Diffusion Based Unpaired Data Learning for Inverse Problems

Data is important in many deep learning-based inverse problem solvers. However, obtaining sufficient paired data in many scenarios remains highly challenging, while unpaired data is cheap. To maximize data utilization, this paper proposes LUD-DIF, a diffusion-based approach for solving inverse problems with unpaired data. Starting from the evidence lower bound (ELBO) of the joint distribution, we decouple it into two independent diffusion processes under the weak-coupling assumption. The method provides theoretical support from a variational inference perspective, derives the loss function, quantitatively analyzes the error bound introduced by the assumption, and offers a theorem-motivated heuristic for hyperparameter selection. Experimental results demonstrate that LUD-DIF achieves outstanding performance on multiple image inverse problems, validating its effectiveness and generalization capability in unpaired inverse problem settings.

Shared Semantic Codebook Distillation for Unpaired Cross-Modal Medical Classification

Cross-modal knowledge distillation can transfer diagnostic knowledge from a strong but costly teacher modality to a cheaper and more deployable student modality. In medical image analysis, however, the two modalities are often unpaired: they are collected from different patient cohorts and occupy geometrically incompatible feature spaces. This makes instance-level distillation invalid and direct feature matching unreliable. To address these challenges, we propose Shared Semantic Codebook Distillation (SSCD), which compares teacher and student representations through a shared discrete codebook. Each image is represented as a distribution over a common, modality-agnostic vocabulary, and knowledge is transferred by aligning these distributions across modalities, both globally and class-conditionally, without requiring paired samples or directly comparable raw features. The codebook is evolved online by exponential moving average and kept diverse through entropy regularization and dead-code restart. At inference, all teacher-side and codebook modules are discarded, leaving only the student encoder and classifier. On two heterogeneous unpaired settings, OCT-to-fundus retinal disease classification and CT-to-chest-X-ray pneumonia classification, SSCD improves the student from 64.5 to 70.2 macro-F1 and from 73.8 to 76.3 macro-F1, respectively, outperforming all evaluated distillation baselines on both settings. Code and pretrained models are available at https://github.com/DillanImans/SSCD-unpaired-distillation

Cross-Modal Knowledge Distillation without Paired Data: Theoretical Foundation and Algorithm

Cross-modal knowledge distillation (CMKD) studies how a (large) teacher model trained on one type of data (e.g., images) can guide a (smaller) student model building on another type of data (e.g., text/audio). Existing CMKD methods often require paired multi-modal data with aligned semantics, but obtaining such paired data are often costly and impractical. To mitigate this limitation, we develop a new CMKD framework for the more challenging setting where paired data are unavailable. In particular, we establish a cross-modal distributional relationship between teacher and student models, which reveals two fundamental quantities governing effective distillation: feature alignment and label alignment. These quantities characterize semantic discrepancy between modalities at the levels of representation and prediction distributions, respectively. Motivated by this insight, we propose a principled framework, with theoretical guarantees, that enables effective cross-modal knowledge distillation by aligning distributions rather than individual samples. Extensive experiments across a wide range of multimodal benchmarks show that our framework is highly effective in both unpaired and paired data settings, improving significantly over prior work.