This work proposes Projected Energy Matching, a scalable framework that resolves structural and computational bottlenecks in energy matching, and introduces Helmholtz Distillation, a structural relaxation that leverages a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network.
Abstract
Energy Matching has emerged as a powerful generative framework that combines flow model efficiency with the explicit likelihood of Energy-Based Models (EBMs) via a single, time-independent scalar potential. However, directly training this potential on high-dimensional 3D data remains computationally challenging. While distilling a pre-trained flow model circumvents some of the initial training costs, we demonstrate that velocity fields inevitably contain non-conservative rotational artifacts (curl). Forcing a strictly conservative scalar potential to match this unconstrained field creates a"structural conflict", which degrades generation quality and mode coverage. To solve this, we propose Projected Energy Matching, a scalable framework that resolves these structural and computational bottlenecks. We introduce Helmholtz Distillation, a structural relaxation that leverages a Hutchinson trace estimator to explicitly absorb rotational noise into an auxiliary residual network. We subsequently refine this landscape using Negative Caching, a memory-efficient strategy that reuses negative samples across micro-batches, rendering sampling tractable during contrastive training with gradient accumulation. We deploy our method as an unconditional prior for real-world medical CT inverse problems, specifically sparse-view reconstruction. Ultimately, our amortized pipeline reduces total compute to a small fraction of that required by standard energy matching, while achieving high-fidelity reconstructions and successfully resolving severe measurement artifacts.
Energy-Guided Flow Matching is introduced that explicitly models a coarse-to-fine generative trajectory by moving endpoint that evolves smoothly from low-frequency image to clean image and requires no adaptation of the backbone and training data.
It is shown in this work that flow matching models with a potential-induced velocity yield an explicit scalar energy at all transport times, whose gradient is exactly the converted learned score and which recovers the marginal negative log-density at the population optimum.
Yixuan Sun, A. Samaddar, Sandeep Madireddy· 0 citations
This paper proposes K-NeAS, a unified and scalable architecture for automated, multi-material surface reconstruction that replaces independent material networks with a shared latent backbone and introduces a fully differentiable $K$-material sequential soft selector to model an arbitrary number of overlapping tissues.
Daksh K. Shah, Emmanouil Nikolakakis, Razvan V. Marinescu· 0 citations
Generative models like Diffusion Models and Flow Matching have demonstrated remarkable capabilities in synthesizing high-fidelity driving videos, but are severely constrained by high inference latency due to the requirement of extensive sampling steps. We argue that this inefficiency stems from the prevailing reliance on a standard Gaussian source distribution, where consecutive frames are initialized as independent Gaussian noise. This paradigm disregards the rich spatiotemporal correlations inherent in driving videos, compelling the model to regenerate deterministic scene structures existing in previous frames from noise, which is both computationally redundant and prone to geometric inconsistency. To address this problem, we propose GeoFlow, a novel framework designed to achieve efficient driving video generation by harnessing explicit geometric priors. Instead of sampling from standard Gaussian noise, we leverage multi-view geometry and spatially-adaptive noise injection to construct a Geometry-Aligned Prior (GAP) distribution as starting point. This initialization bridges the gap between source distribution and data distribution, yielding a significantly straighter and shorter sampling trajectory. Extensive experiments demonstrate that GeoFlow can achieve remarkable efficiency of both training and inference: merely several hours of fine-tuning on baseline models can significantly boost few-step generation quality, while fully converged training drastically reduces number of inference steps required for state-of-the-art video generation.
Jiazheng Liu, Hangbiao Li, J. Zhang et al.· 0 citations
3D Gaussian Splatting (3DGS) achieves state-of-the-art rendering quality at real-time speeds but suffers from"model bloat"- a large number of redundant, low-opacity Gaussians that inflate memory usage and training costs. This inefficiency stems from the standard"densify-then-prune"paradigm, which expands the model aggressively before relying on pruning to achieve compactness. To mitigate this problem, we present an efficient training framework that builds an intrinsically compact representation, replacing the conventional densify-then-prune cycle. Our method leverages a synergistic design: an L2 reconstruction loss to provide error-proportional gradients that stabilize optimization, and a novel Polarized Opacity Prior (POP) to actively manage the Gaussian population. POP steers informative primitives toward full opacity and uninformative ones toward transparency, enabling natural pruning and accelerating rendering through Early Ray Termination. Experiments on three public datasets demonstrate that our approach consistently achieves accelerated 3DGS training with significantly fewer Gaussians while maintaining comparable visual reconstruction quality. These results show that the proposed framework provides a simple and effective path toward fast and inherently compact 3DGS training.
Zi-Ming Wang, Kai-Wen Duan, Kowei Huang et al.· 0 citations
Full-body capture from unconstrained photographs requires global correspondence across arbitrary views, poses, crops, and occlusions. Yet pose, geometry, and foundation features estimated in this setting are too unreliable for dense matching or appearance transfer, while diffusion rectifiers and optimization pipelines expose no common interface for consuming such uncertain correspondence. Our insight is that correspondence need not be locally accurate: its coarse viewpoint and body layout can still organize how a diffusion prior adapts and guides reconstruction. We introduce \emph{Astrolabe}, a host-portable adapter built on frozen viewpoint-guided spherical maps (SPH). A fixed bounded transform converts SPH into a spatial noise shift, which is matched during prior adaptation and reused during downstream denoising or score-distillation guidance in both pipeline categories. When a rectifier exposes a reference router, the same target/reference SPH additionally supplies coarse compatibility scores to select native appearance features; router-free optimization uses only the shared shift path. Astrolabe therefore follows one SPH--shift--adapt--guide process without dense warping or a learned control branch. Across Puzzle-IOI and 4D-Dress, it improves all reported image metrics in both hosts and all paired Puzzle-IOI geometry metrics; image gains extend to rear views, while 4D-Dress geometry remains stable overall.
Shuliang Zhu, Qi Wang, Ryugo Morita et al.· 0 citations