This paradigm has been challenged by practical deployments, which are more dynamic in nature.

We introduce Guided Harmonic Path-Integral Diffusion (GH-PID), a linearly-solvable framework for guided Stochastic Optimal Transport (SOT) with a hard terminal distribution and soft, application-driven path costs. A low-dimensional guidance protocol shapes the trajectory ensemble while preserving analytic structure: the forward and backward Kolmogorov equations remain linear, the optimal score admits an explicit Green-function ratio, and Gaussian-Mixture Model (GMM) terminal laws yield closed-form expressions. This enables stable sampling and differentiable protocol learning under exact terminal matching. We develop guidance-centric diagnostics -- path cost, centerline adherence, variance flow, and drift effort -- that make GH-PID an interpretable variational ansatz for empirical SOT. Three navigation scenarios illustrated in 2D: (i) Case A: hand-crafted protocols revealing how geometry and stiffness shape lag, curvature effects, and mode evolution; (ii) Case B: single-task protocol learning, where a PWC centerline is optimized to minimize integrated cost; (iii) Case C: multi-expert fusion, in which a commander reconciles competing expert/teacher trajectories and terminal beliefs through an exact product-of-experts law and learns a consensus protocol. Across all settings, GH-PID generates geometry-aware, trust-aware trajectories that satisfy the prescribed terminal distribution while systematically reducing integrated cost.

Diffusion-based samplers -- Score Based Diffusions, Bridge Diffusions and Path Integral Diffusions -- match a target at terminal time, but the real leverage comes from choosing the schedule that governs the intermediate-time dynamics. We develop a path-wise schedule -- selection gramework for Harmonic PID with a time-varying stiffness, exploiting Piece-Wise-Constant(PWC) parametrizations and a simple hierarchical refinement. We introduce schedule-sensitive Quality-of-Sampling (QoS) diagnostics. Assuming a Gaussian-Mixture (GM) target, we retain closed-form Green functions' ration and numerically stable, Neural-Network free oracles for predicted-state maps and score. Experiments in 2D show that QoS driven PWC schedules consistently improve early-exit fidelity, tail accuracy, conditioning of the dynamics, and speciation (label-selection) timing at fixed integration budgets.

Unlearning in large foundation models (e.g., LLMs) is essential for enabling dynamic knowledge updates, enforcing data deletion rights, and correcting model behavior. However, existing unlearning methods often require full-model fine-tuning or access to the original training data, which limits their scalability and practicality. In this work, we introduce Recover-to-Forget (R2F), a novel framework for efficient unlearning in LLMs based on reconstructing full-model gradient directions from low-rank LoRA adapter updates. Rather than performing backpropagation through the full model, we compute gradients with respect to LoRA parameters using multiple paraphrased prompts and train a gradient decoder to approximate the corresponding full-model gradients. To ensure applicability to larger or black-box models, the decoder is trained on a proxy model and transferred to target models. We provide a theoretical analysis of cross-model generalization and demonstrate that our method achieves effective unlearning while preserving general model performance. Experimental results demonstrate that R2F offers a scalable and lightweight alternative for unlearning in pretrained LLMs without requiring full retraining or access to internal parameters.

Recently, Multi-Contrast MR Reconstruction (MCMR) has emerged as a hot research topic that leverages high-quality auxiliary modalities to reconstruct undersampled target modalities of interest. However, existing methods often struggle to generalize across different k-space undersampling patterns, requiring the training of a separate model for each specific pattern, which limits their practical applicability. To address this challenge, we propose UniFS, a Unified Frequency-Spatial Fusion model designed to handle multiple k-space undersampling patterns for MCMR tasks without any need for retraining. UniFS integrates three key modules: a Cross-Modal Frequency Fusion module, an Adaptive Mask-Based Prompt Learning module, and a Dual-Branch Complementary Refinement module. These modules work together to extract domain-invariant features from diverse k-space undersampling patterns while dynamically adapt to their own variations. Another limitation of existing MCMR methods is their tendency to focus solely on spatial information while neglect frequency characteristics, or extract only shallow frequency features, thus failing to fully leverage complementary cross-modal frequency information. To relieve this issue, UniFS introduces an adaptive prompt-guided frequency fusion module for k-space learning, significantly enhancing the model's generalization performance. We evaluate our model on the BraTS and HCP datasets with various k-space undersampling patterns and acceleration factors, including previously unseen patterns, to comprehensively assess UniFS's generalizability. Experimental results across multiple scenarios demonstrate that UniFS achieves state-of-the-art performance. Our code is available at https://github.com/LIKP0/UniFS.

Cross-Domain Offline Reinforcement Learning aims to train an agent deployed in the target environment, leveraging both a limited target domain dataset and a source domain dataset with (possibly) sufficient data coverage. Due to the underlying dynamics misalignment between the source and target domain, simply merging the data from two datasets may incur inferior performance. Recent advances address this issue by selectively sharing source domain samples that exhibit dynamics alignment with the target domain. However, these approaches focus solely on dynamics alignment and overlook \textit{value alignment}, i.e., selecting high-quality, high-value samples from the source domain. In this paper, we first demonstrate that both dynamics alignment and value alignment are essential for policy learning, by examining the limitations of the current theoretical framework for cross-domain RL and establishing a concrete sub-optimality gap of a policy trained on the source domain and evaluated on the target domain. Motivated by the theoretical insights, we propose to selectively share those source domain samples with both high dynamics and value alignment and present our \textbf{\underline{D}}ynamics- and \textbf{\underline{V}}alue-aligned \textbf{\underline{D}}ata \textbf{\underline{F}}iltering (DVDF) method. We design a range of dynamics shift settings, including kinematic and morphology shifts, and evaluate DVDF on various tasks and datasets, as well as in challenging extremely low-data settings where the target domain dataset contains only 5,000 transitions. Extensive experiments demonstrate that DVDF consistently outperforms prior strong baselines and delivers exceptional performance across multiple tasks and datasets.

Generative models for structure-based drug design are often limited to a specific modality, restricting their broader applicability. To address this challenge, we introduce FuncBind, a framework based on computer vision to generate target-conditioned, all-atom molecules across atomic systems. FuncBind uses neural fields to represent molecules as continuous atomic densities and employs score-based generative models with modern architectures adapted from the computer vision literature. This modality-agnostic representation allows a single unified model to be trained on diverse atomic systems, from small to large molecules, and handle variable atom/residue counts, including non-canonical amino acids. FuncBind achieves competitive in silico performance in generating small molecules, macrocyclic peptides, and antibody complementarity-determining region loops, conditioned on target structures. FuncBind also generated in vitro novel antibody binders via de novo redesign of the complementarity-determining region H3 loop of two chosen co-crystal structures. As a final contribution, we introduce a new dataset and benchmark for structure-conditioned macrocyclic peptide generation. The code is available at https://github.com/prescient-design/funcbind.

To this end, we propose evaluating the robustness of open-source large VLMs in the most realistic and high-risk setting, where adversaries have only black-box system access and seek to deceive the model into returning the targeted responses.