Lateral-Axial Factorization Architecture
Figure 2: Visual illustration of the proposed lateral–axial factorization. Unlike standard 3D convolutions, our architecture applies lateral and axial convolutions separately, followed by attention modules along their respective dimensions. This factorization improves scalability by enabling deeper networks under the same GPU memory budget; see comparison in Fig. 5 .
Paper context
Paper title: VOLT: Volumetric Wide-Field Microscopy via 3D-Native Probabilistic Transport Abstract: Three-dimensional (3D) wide-field fluorescence microscopy is a widely used modality for volumetric imaging, but suffers from characteristic out-of-focus blur. Existing reconstruction methods either struggle to operate on high-dimensional volumes or fail to provide credibility characterization of the reconstruction. In this work, we introduce Volumetric Transport (VOLT), a 3D-native probabilistic framework for wide-field fluorescence microscopy reconstruction. VOLT combines a transport-based formulation that maps degraded measurements to clean volumes via stochastic interpolants with a 3D-native anisotropic network that separates lateral and axial processing. This design operates directly in voxel space and achieves improved scalability to large volumes without relying on slice-wise approximations. We develop both stochastic (SDE) and deterministic (ODE) variants within the same framework. We validate VOLT on simulated wide-field microscopy datasets. Our results show that VOLT significantly improves reconstruction quality in both lateral and axial directions while providing voxel-wise credibility estimates. Passages referencing this figure: transport between two distributions. However, directly processing 3D volumes within these frameworks remains a computational challenge. Existing methods either rely on 2D slice-wise processing that can be suboptimal for axial information recovery [ 23 , 17 , 24 ] , or learn a separate image encoder and decoder to operate in a low-dimensional latent space [ 25 , 26 ] , which can be hard to train. Figure 1: Conceptual illustration of the proposed VOLT framework for wide-field fluorescence microscopy. The bottom portion illustrates the imaging process, where the camera captures a blurred 3D volume by axially scanning the specimen. The top portion depicts VOLT, which employs a 3D-native network to probabilistically transport the degraded measurement to a clean volume. Unlike existing methods, section, we introduce the forward model for wide-field fluorescence microscopy and review reconstruction methods ranging from classical model-based methods to deep generative models. 2.1 Inverse Problem in Wide-Field Fluorescence Microscopy Wide-field fluorescence microscopy illuminates the entire specimen at once, collecting emitted light across the full field of view through the objective lens; Fig. 1 provides a schematic illustration. The acquisition process can be described by the 3D emission point spread function (PSF) h ( x , y , z ) h(x,y,z) , which characterizes how the optical system blurs a single point emitter [ 34 ] h ( x , y , z ) = | ℱ [ P ( k x , k y ) exp ( i 2 π λ em ϕ ( k x , k y ) ) × exp ( − 2 π i z n 0 2 λ em 2 − k x 2 − k y 2 ) ] | 2 , \begin{split}h(x,y,z)&
