Diffusion bridge models and stochastic interpolants enable high-quality imageto-image (I2I) translation by creating paths between distributions in pixel space. However, recent diffusion bridge models excel in image translation but suffer from restricted design flexibility and complicated hyperparameter tuning, whereas Stochastic Interpolants offer greater flexibility but lack essential refinements. We show that these complementary strengths can be unified by interpreting all existing methods within a single SI-based framework. In this work, we unify and expand the space of bridge models by extending Stochastic Interpolants (SIs) with preconditioning, endpoint conditioning, and an optimized sampling algorithm. These enhancements expand the design space of diffusion bridge models, leading to state-of-the-art performance in both image quality and sampling efficiency across diverse I2I tasks. Furthermore, we identify and address a previously overlooked issue of low sample diversity under fixed conditions. We introduce a quantitative analysis for output diversity and demonstrate how we can modify the base distribution for further improvements. Code is available at https://github.com/szhan311/ECSI.

Diffusion bridge models and stochastic interpolants enable high-quality image-to-image (I2I) translation by creating paths between distributions in pixel space. However, recent diffusion bridge models excel in image translation but suffer from restricted design flexibility and complicated hyperparameter tuning, whereas Stochastic Interpolants offer greater flexibility but lack essential refinements. We show that these complementary strengths can be unified by interpreting all existing methods within a single SI-based framework. In this work, we unify and expand the space of bridge models by extending Stochastic Interpolants (SIs) with preconditioning, endpoint conditioning, and an optimized sampling algorithm. These enhancements expand the design space of diffusion bridge models, leading to state-of-the-art performance in both image quality and sampling efficiency across diverse I2I tasks. Furthermore, we identify and address a previously overlooked issue of low sample diversity under fixed conditions. We introduce a quantitative analysis for output diversity and demonstrate how we can modify the base distribution for further improvements.

Inverse protein folding is a fundamental task in computational protein design, which aims to design protein sequences that fold into the desired backbone structures. While the development of machine learning algorithms for this task has seen significant success, the prevailing approaches, which predominantly employ a discriminative formulation, frequently encounter the error accumulation issue and often fail to capture the extensive variety of plausible sequences. To fill these gaps, we propose Bridge-IF, a generative diffusion bridge model for inverse folding, which is designed to learn the probabilistic dependency between the distributions of backbone structures and protein sequences. Specifically, we harness an expressive structure encoder to propose a discrete, informative prior derived from structures, and establish a Markov bridge to connect this prior with native sequences.

These approaches employ a refinement module to identify and correct inaccurately predicted amino acids.

Bridge models have recently been explored for speech enhancement tasks such as denoising, dereverberation, and super-resolution, while these efforts are typically confined to a single task or small-scale datasets, with constrained general speech restoration (GSR) capability at scale. In this work, we introduce VoiceBridge, a GSR system rooted in latent bridge models (LBMs), capable of reconstructing high-fidelity speech at full-band (\textit{i.e.,} 48~kHz) from various distortions. By compressing speech waveform into continuous latent representations, VoiceBridge models the~\textit{diverse LQ-to-HQ tasks} (namely, low-quality to high-quality) in GSR with~\textit{a single latent-to-latent generative process} backed by a scalable transformer architecture. To better inherit the advantages of bridge models from the data domain to the latent space, we present an energy-preserving variational autoencoder, enhancing the alignment between the waveform and latent space over varying energy levels. Furthermore, to address the difficulty of HQ reconstruction from distinctively different LQ priors, we propose a joint neural prior, uniformly alleviating the reconstruction burden of LBM. At last, considering the key requirement of GSR systems, human perceptual quality, a perceptually aware fine-tuning stage is designed to mitigate the cascading mismatch in generation while improving perceptual alignment. Extensive validation across in-domain and out-of-domain tasks and datasets (\textit{e.g.}, refining recent zero-shot speech and podcast generation results) demonstrates the superior performance of VoiceBridge. Demo samples can be visited at: https://VoiceBridge-demo.github.io/.

The essence of a chemical reaction lies in the redistribution and reorganization of electrons, which is often manifested through electron transfer or the migration of electron pairs. These changes are inherently discrete and abrupt in the physical world, such as alterations in the charge states of atoms or the formation and breaking of chemical bonds. To model the transition of states, we propose SynBridge, a bidirectional flow-based generative model to achieve multi-task reaction prediction. By leveraging a graph-to-graph transformer network architecture and discrete flow bridges between any two discrete distributions, SynBridge captures bidirectional chemical transformations between graphs of reactants and products through the bonds' and atoms' discrete states. We further demonstrate the effectiveness of our method through extensive experiments on three benchmark datasets (USPTO-50K, USPTO-MIT, Pistachio), achieving state-of-the-art performance in both forward and retrosynthesis tasks. Our ablation studies and noise scheduling analysis reveal the benefits of structured diffusion over discrete spaces for reaction prediction.

Inverse protein folding is a fundamental task in computational protein design, which aims to design protein sequences that fold into the desired backbone structures. While the development of machine learning algorithms for this task has seen significant success, the prevailing approaches, which predominantly employ a discriminative formulation, frequently encounter the error accumulation issue and often fail to capture the extensive variety of plausible sequences. To fill these gaps, we propose Bridge-IF, a generative diffusion bridge model for inverse folding, which is designed to learn the probabilistic dependency between the distributions of backbone structures and protein sequences. Specifically, we harness an expressive structure encoder to propose a discrete, informative prior derived from structures, and establish a Markov bridge to connect this prior with native sequences. Moreover, we introduce a reparameterization perspective on Markov bridge models, from which we derive a simplified loss function that facilitates more effective training.

Recent studies have shown that diffusion models produce superior synthetic images when compared to Generative Adversarial Networks (GANs). However, their outputs are often non-deterministic and lack high fidelity to the ground truth due to the inherent randomness. In this paper, we propose a novel High-fidelity Brownian bridge model (HiFi-BBrg) for deterministic medical image translations. Our model comprises two distinct yet mutually beneficial mappings: a generation mapping and a reconstruction mapping. The Brownian bridge training process is guided by the fidelity loss and adversarial training in the reconstruction mapping. This ensures that translated images can be accurately reversed to their original forms, thereby achieving consistent translations with high fidelity to the ground truth. Our extensive experiments on multiple datasets show HiFi-BBrg outperforms state-of-the-art methods in multi-modal image translation and multi-image super-resolution.

In-silico material discovery and design have traditionally relied on high-fidelity first-principles methods such as density functional theory (DFT) [1] and ab-initio molecular dynamics (AIMD) [2] to accurately model atomic interactions and predict material properties. Despite their effectiveness, these methods face significant challenges due to their prohibitive computational cost, limiting their scalability for highthroughput screening across vast chemical spaces and for simulations over large length and time scales. Moreover, many advanced materials remain beyond the reach of widespread predictive theories due to a fundamental lack of mechanistic understanding. These challenges stem from the inherent complexity of their chemical composition, phase stability, and the intricate interplay of multiple order parameters, compounded by the lack of self-consistent integration between theoretical models and multi-modal experimental findings. As a result, breakthroughs in functional materials, such as new classes of correlated oxides, nitrides, and low-dimensional quantum materials, have largely been serendipitous or guided by phenomenological intuition rather than systematic, theory-driven design. Attempts to predict new materials and functionalities have often led to mixed results, with theoretically proposed systems failing to exhibit the desired properties when synthesized and tested.