We propose a novel regularization loss that enforces standard Gaussianity, encouraging samples to align with a standard Gaussian distribution. This facilitates a range of downstream tasks involving optimization in the latent space of text-to-image models. We treat elements of a high-dimensional sample as one-dimensional standard Gaussian variables and define a composite loss that combines moment-based regularization in the spatial domain with power spectrum-based regularization in the spectral domain. Since the expected values of moments and power spectrum distributions are analytically known, the loss promotes conformity to these properties. To ensure permutation invariance, the losses are applied to randomly permuted inputs. Notably, existing Gaussianity-based regularizations fall within our unified framework: some correspond to moment losses of specific orders, while the previous covariance-matching loss is equivalent to our spectral loss but incurs higher time complexity due to its spatial-domain computation. We showcase the application of our regularization in generative modeling for test-time reward alignment with a text-to-image model, specifically to enhance aesthetics and text alignment. Our regularization outperforms previous Gaussianity regularization, effectively prevents reward hacking and accelerates convergence.

We propose an inference-time scaling approach for pretrained flow models. Recently, inference-time scaling has gained significant attention in LLMs and diffusion models, improving sample quality or better aligning outputs with user preferences by leveraging additional computation. For diffusion models, particle sampling has allowed more efficient scaling due to the stochasticity at intermediate denoising steps. On the contrary, while flow models have gained popularity as an alternative to diffusion models--offering faster generation and high-quality outputs--efficient inference-time scaling methods used for diffusion models cannot be directly applied due to their deterministic generative process. To enable efficient inference-time scaling for flow models, we propose three key ideas: 1) SDE-based generation, enabling particle sampling in flow models, 2) Interpolant conversion, broadening the search space and enhancing sample diversity, and 3) Rollover Budget Forcing (RBF), an adaptive allocation of computational resources across timesteps to maximize budget utilization. Our experiments show that SDE-based generation and variance-preserving (VP) interpolant-based generation, improves the performance of particle sampling methods for inference-time scaling in flow models. Additionally, we demonstrate that RBF with VP-SDE achieves the best performance, outperforming all previous inference-time scaling approaches.

We introduce Neural Green’s Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green’s functions, the solution operators of linear PDEs that depend exclusively on the domain geometry, we design Neural Green’s Function to imitate their behavior, achieving superior generalization across diverse irregular geometries and source and boundary functions. Specifically, Neural Green’s Function extracts per-point features from a volumetric point cloud representing the problem domain and uses them to predict a decomposition of the solution operator, which is subsequently applied to evaluate solutions via numerical integration. Unlike recent learning-based solution operators, which often struggle to generalize to unseen source or boundary functions, our framework is, by design, agnostic to the specific functions used during training, enabling robust and efficient generalization. In the steady-state thermal analysis of mechanical part geometries from the MCB dataset, Neural Green’s Function outperforms state-of-the-art neural operators, achieving an average error reduction of 13.9% across five shape categories, while being up to 350 times faster than a numerical solver that requires computationally expensive meshing.

We introduce a dual contouring method that provides state-of-the-art performance for occupancy functions while achieving computation times of a few seconds. Our method is learning-free and carefully designed to maximize the use of GPU parallelization. The recent surge of implicit neural representations has led to significant attention to occupancy fields, resulting in a wide range of 3D reconstruction and generation methods based on them. However, the outputs of such methods have been underestimated due to the bottleneck in converting the resulting occupancy function to a mesh. Marching Cubes tends to produce staircase-like artifacts, and most subsequent works focusing on exploiting signed distance functions as input also yield suboptimal results for occupancy functions. Based on Manifold Dual Contouring (MDC), we propose Occupancy-Based Dual Contouring (ODC), which mainly modifies the computation of grid edge points (1D points) and grid cell points (3D points) to not use any distance information. We introduce auxiliary 2D points that are used to compute local surface normals along with the 1D points, helping identify 3D points via the quadric error function. To search the 1D, 2D, and 3D points, we develop fast algorithms that are parallelizable across all grid edges, faces, and cells. Our experiments with several 3D neural generative models and a 3D mesh dataset demonstrate that our method achieves the best fidelity compared to prior works.