Diffusion models typically generate image batches from independent Gaussian initial noises. We argue that this independence assumption is only one choice within a broader class of valid joint noise designs. Instead, one can specify a coupling of the initial noises: each noise remains marginally standard Gaussian, so the pretrained diffusion model receives the same single-sample input distribution, while the dependence across samples is chosen by design. This reframes initial-noise control from selecting or optimizing individual seeds to designing the dependence structure of a multi-sample gallery. This view gives a general framework for initial-noise design, covering several existing methods as special cases and leading naturally to new coupled-noise constructions. Coupled noise can improve generation on its own without adding sampling cost, and it is flexible enough to serve as a structured initialization for optimization-based pipelines when additional computation is available. Empirically, repulsive Gaussian coupling improves gallery diversity on SD1.5, SDXL, and SD3 while largely preserving prompt alignment and image quality. It matches or outperforms recent test-time noise-optimization baselines on several diversity metrics at the same sampling cost as independent generation. Subspace couplings also support fixed-object background generation, producing diverse, natural backgrounds compared with specialized inpainting baselines, with a tunable trade-off in foreground fidelity.

Reinforcement Learning with Verifiable Rewards (RLVR) has achieved substantial gains in single-attempt accuracy (Pass@1) on reasoning tasks, yet often suffers from reduced multi-sample coverage (Pass@K), indicating diversity collapse. We identify a structural cause for this degradation: common RLVR objectives, such as GRPO, are indifferent to how probability mass is distributed among correct solutions. Combined with stochastic training dynamics, this indifference induces a self-reinforcing collapse, in which probability mass concentrates on a narrow subset of correct outputs while alternative valid solutions are suppressed. We formalize this collapse mechanism and further characterize the optimal policy structure under two complementary criteria: robustness and entropy-regularized optimality, which identify the Uniform-Correct Policy as uniquely optimal. Motivated by this analysis, we propose Uniform-Correct Policy Optimization (UCPO), a modification to GRPO that adds a conditional uniformity penalty on the policy's distribution over correct solutions. The penalty redistributes gradient signal toward underrepresented correct responses, encouraging uniform allocation of probability mass within the correct set. Across three models (1.5B-7B parameters) and five mathematical reasoning benchmarks, UCPO improves Pass@K and diversity while maintaining competitive Pass@1, achieving up to +10\% absolute improvement on AIME24 at Pass@64 and up to 45\% higher equation-level diversity within the correct set. The code is available at https://github.com/AnamikaLochab/UCPO.

Despite remarkable performance in producing realistic samples, Generative Adversarial Networks (GANs) often produce low-quality samples near low-density regions of the data manifold, e.g., samples of minor groups. Many techniques have been developed to improve the quality of generated samples, either by postprocessing generated samples or by pre-processing the empirical data distribution, but at the cost of reduced diversity. To promote diversity in sample generation without degrading the overall quality, we propose a simple yet effective method to diagnose and emphasize underrepresented samples during training of a GAN. The main idea is to use the statistics of the discrepancy between the data distribution and the model distribution at each data instance. Based on the observation that the underrepresented samples have a high average discrepancy or high variability in discrepancy, we propose a method to emphasize those samples during training of a GAN. Our experimental results demonstrate that the proposed method improves GAN performance on various datasets, and it is especially effective in improving the quality and diversity of sample generation for minor groups.

We present the HOH (Human-Object-Human) Handover Dataset, a large object count dataset with 136 objects, to accelerate data-driven research on handover studies, human-robot handover implementation, and artificial intelligence (AI) on handover parameter estimation from 2D and 3D data of two-person interactions. HOH contains multi-view RGB and depth data, skeletons, fused point clouds, grasp type and handedness labels, object, giver hand, and receiver hand 2D and 3D segmentations, giver and receiver comfort ratings, and paired object metadata and aligned 3D models for 2,720 handover interactions spanning 136 objects and 20 giver-receiver pairs--40 with role-reversal--organized from 40 participants. We also show experimental results of neural networks trained using HOH to perform grasp, orientation, and trajectory prediction. As the only fully markerless handover capture dataset, HOH represents natural human-human handover interactions, overcoming challenges with markered datasets that require specific suiting for body tracking, and lack high-resolution hand tracking. To date, HOH is the largest handover dataset in terms of object count, participant count, pairs with role reversal accounted for, and total interactions captured.

Protein inverse folding has attracted increasing attention in recent years. However, we observe that current methods are usually limited to the CATH dataset and the recovery metric. The lack of a unified framework for ensembling and comparing different methods hinders the comprehensive investigation. In this paper, we propose ProteinInvBench, a new benchmark for protein design, which comprises extended protein design tasks, integrated models, and diverse evaluation metrics. We broaden the application of methods originally designed for single-chain protein design to new scenarios of multi-chain and de novo protein design. Recent impressive methods, including GraphTrans, StructGNN, GVP, GCA, AlphaDesign, ProteinMPNN, PiFold and KWDesign are integrated into our framework. In addition to the recovery, we also evaluate the confidence, diversity, sc-TM, efficiency, and robustness to thoroughly revisit current protein design approaches and inspire future work. As a result, we establish the first comprehensive benchmark for protein design, which is publicly available at https://github.com/A4Bio/OpenCPD.