DiGS: Diverse Methods & Applications

• DiGS is a multifaceted acronym defining methods such as divergence-guided implicit neural representations for 3D surface reconstruction from unoriented point clouds.
• It also denotes geometry-aware 3D Gaussian splatting techniques that couple learnable signed distance functions with opacity-driven rendering to recover high-fidelity surfaces.
• Additionally, DiGS refers to methodologies like Diffusive Gibbs Sampling for improved multimodal MCMC and clinical datasets in ophthalmic OCT analysis.

DiGS is not a single research object but a recurring acronym used for several unrelated constructs across contemporary technical literature. The papers considered here show that it can denote a divergence-regularized neural signed-distance framework for surface reconstruction from unoriented point clouds (Ben-Shabat et al., 2021), a geometry-aware 3D Gaussian Splatting method that embeds direct SDF learning into the rendering pipeline (Guo et al., 9 Sep 2025), and a multimodal MCMC family called Diffusive Gibbs Sampling (Chen et al., 2024). In other domains, closely related uppercase forms denote the Diagnostic Innovations in Glaucoma Study cohort used for OCT interpretation (Jalili et al., 1 Oct 2025), a five-level dressed atomic system for refractive-index engineering (Sagona-Stophel et al., 2011), a neural-posterior framework for galaxy spectra (Khullar et al., 2022), and a deformation-informed 4D Gaussian-splatting method for dynamic CBCT reconstruction (Huang et al., 27 Jun 2025). Disambiguation is therefore essential.

1. Nomenclature and scope

The acronym is used heterogeneously, and identical capitalization does not imply a common method family.

Name in paper	Expansion or usage	Domain
DiGS	Divergence guided Shape implicit neural representation	Neural SDF learning from unoriented point clouds
DiGS	Accurate and Complete Surface Reconstruction from 3D Gaussians via Direct SDF Learning	Geometry-aware 3D Gaussian Splatting
DiGS	Diffusive Gibbs Sampling	Multimodal MCMC
DIGS	Diagnostic Innovations in Glaucoma Study	Ophthalmic cohort
DIGS	Deep Inference of Galaxy Spectra	Simulation-based inference for galaxy SEDs
DIGS atoms	Five level DIGS atoms	Atomic optics and refractive-index engineering
DIGS	Dynamic CBCT reconstruction using deformation-informed 4D Gaussian splatting	Medical image reconstruction

A common misconception is to treat “DiGS” as a single geometry method. In the literature represented here, that is accurate only for a subset of papers. The 2021 DiGS paper concerns sinusoidal implicit neural representations for unoriented point clouds (Ben-Shabat et al., 2021), whereas the 2025 DiGS paper concerns 3D Gaussian Splatting with direct SDF learning (Guo et al., 9 Sep 2025). By contrast, the ophthalmic DIGS paper uses the acronym as a cohort name rather than as an algorithmic framework (Jalili et al., 1 Oct 2025).

2. DiGS as divergence-guided shape implicit neural representation

In its best-defined machine-learning usage, DiGS stands for Divergence guided Shape implicit neural representation and is designed to learn signed distance functions (SDFs) of 3D shapes from unoriented point clouds (Ben-Shabat et al., 2021). The method learns an implicit function $\Phi(x;\theta)$ whose zero level set represents the surface,

$$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$

Its central claim is that, when normals are unavailable or unreliable, one can regularize the learned SDF by penalizing the divergence of the gradient field away from the surface: $$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$ This term is combined with manifold, Eikonal, and non-manifold losses: $$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$ with $\lambda_{div}=100$ and an annealing factor $\tau$.

The method is not only a loss design. A second contribution is a geometric initialization for SIRENs that makes the initial field approximately spherical,

$\Phi(x;\theta_0) \approx \|x\|_2 - r,$

together with a multi-frequency geometric initialization (MFGI) that mixes low-frequency sphere-like structure with high-frequency capacity. Training follows a smooth-to-sharp curriculum: roughly 50% high divergence, 25% annealing, and 25% low divergence. The paper also reports that an $L_1$ divergence penalty is better than $L_2$, because it allows localized regions of high divergence.

Empirically, DiGS is presented as SOTA among unoriented / no-normal methods on surface reconstruction benchmarks and as competitive with some normal-supervised methods on SRB and ShapeNet, while also being usable as an autodecoder for DFaust (Ben-Shabat et al., 2021). At the same time, its limitations are explicit: thin structures can be missed, the divergence prior can induce over-smoothing, and internal ghost geometry can remain on shapes with complex internal structure. Later work by ViscoReg positions DiGS as a strong normal-free baseline but argues that directly minimizing divergence or Laplacian-like quantities can be harmful in regions with fine geometric detail because the Laplacian/divergence of an SDF is tied to mean curvature (Krishnan et al., 1 Jul 2025). In the ViscoReg comparison on SRB, the table reports DiGS: $d_C=0.19$, $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$0, while the quadratic ViscoReg schedule reaches $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$1, $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$2; on ShapeNet, DiGS is reported at squared Chamfer $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$3, IoU $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$4. This establishes DiGS as a consequential prior baseline precisely because its curvature-smoothing bias is both effective and potentially detail-suppressing.

3. DiGS as direct SDF learning in 3D Gaussian Splatting

A distinct 2025 usage of the name introduces DiGS as a geometry-aware 3D Gaussian Splatting framework that recovers accurate, complete surfaces while preserving high rendering fidelity (Guo et al., 9 Sep 2025). Here the primitives are anisotropic Gaussians

$$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$5

each with center $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$6, covariance $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$7, color $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$8, and opacity $$\mathcal{S} = \{x \in \mathbb{R}^3 : \Phi(x;\theta)=0\}.$$9. The key departure from appearance-driven 3DGS is that each Gaussian is associated with a learnable signed distance value, so the surface is represented as the zero level set

$$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$0

The SDF is coupled directly to opacity: $$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$1 which encourages Gaussians to remain near the surface because off-surface primitives become visually less relevant.

The representation is multi-scale. DiGS initializes a hierarchical octree / LoD grid with voxel size

$$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$2

places $$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$3 Gaussians per occupied voxel, interpolates features by inverse-distance weighting, and decodes them with an MLP into primitive attributes including the SDF value. Its second major ingredient is geometry-guided grid growth, triggered at iteration $$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$4. At that point, dense depth and normal maps are estimated for each training view, grazing-angle points are removed, filtered depth maps are back-projected to 3D, and new occupied grid cells are inserted at the coarsest possible level that does not already contain a primitive. Newly inserted Gaussians are given a surface-aligned covariance

$$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$5

typically with $$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$6, and later pruned if opacity is low or $$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$7.

Optimization combines geometry and appearance terms. The SDF center loss,

$$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$8

and the Eikonal loss,

$$L_{div} = \int_{\Omega \setminus \Omega_0} \left| \Delta \Phi(x;\theta) \right| dx = \int_{\Omega \setminus \Omega_0} \left| \nabla_x \cdot \nabla_x \Phi(x;\theta) \right| dx.$$9

are combined with a flattening loss and an RGB reconstruction loss into the total objective. On DTU, the paper reports a mean CD of about 0.46 mm; on Tanks & Temples, it reports the best mean F1 among the compared methods; and on Mip-NeRF 360, it reports competitive PSNR, SSIM, and LPIPS while improving geometric quality (Guo et al., 9 Sep 2025). Unlike the 2021 DiGS, this framework is not about divergence-regularized SIRENs for unoriented point clouds; it is a unified geometry-and-appearance formulation inside the 3DGS pipeline.

4. DiGS as Diffusive Gibbs Sampling

In probabilistic computation, DiGS denotes Diffusive Gibbs Sampling, an MCMC family for multimodal target distributions characterized by distant or disconnected modes (Chen et al., 2024). The target is written as

$$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$0

and the method introduces an auxiliary Gaussian-corrupted variable

$$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$1

Rather than sampling the noisy marginal $$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$2 directly, DiGS samples from the joint

$$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$3

by alternating a noising step and a denoising step. The denoising posterior is

$$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$4

with tractable score

$$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$5

This permits MALA or HMC in the denoising stage.

A practical contribution is a Metropolis-within-Gibbs initialization for the denoising chain, using

$$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$6

followed by an MH correction. The paper also introduces a variance-preserving (VP) noise schedule with

$$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$7

The theoretical statement given is that, for an absolutely continuous target and $$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$8, DiGS yields a $$L_{DiGS} = L_{SIREN\ wo\ n} + \tau \lambda_{div} L_{div},$$9-irreducible and recurrent Markov chain.

The empirical case for DiGS is built around improved mode coverage relative to local samplers and to parallel tempering. On the 40-mode 2D MoG, the reported results are MALA: MMD $\lambda_{div}=100$0, MAE $\lambda_{div}=100$1, HMC: MMD $\lambda_{div}=100$2, MAE $\lambda_{div}=100$3, PT: MMD $\lambda_{div}=100$4, MAE $\lambda_{div}=100$5, and DiGS: MMD $\lambda_{div}=100$6, MAE $\lambda_{div}=100$7. For a 3-layer ReLU Bayesian neural network with 550 parameters, predictive NLL is reported as 0.199$\lambda_{div}=100$8 for DiGS versus 0.261$\lambda_{div}=100$9 for PT. For alanine dipeptide, DiGS reports the lowest KL among the non-ground-truth methods on $\tau$0, $\tau$1, and the joint Ramachandran distribution. In this usage, “DiGS” is unrelated to SDF learning and instead names a Gibbs sampler built around Gaussian convolution.

5. DIGS as the Diagnostic Innovations in Glaucoma Study

In ophthalmology, DIGS denotes the Diagnostic Innovations in Glaucoma Study, a longitudinal cohort used together with ADAGES in work on OCT interpretation by a fine-tuned multimodal LLM (Jalili et al., 1 Oct 2025). In that study, DIGS and ADAGES supply standardized Spectralis optic nerve head (ONH) OCT circle scans and eye-level diagnostic labels. The retrospective dataset spans 2008–2021 and includes 43,849 Spectralis ONH OCT circle scans from 1,310 participants, representing 1,331 glaucomatous eyes and 867 healthy eyes in the abstract summary. Later, the paper also describes the data at the eye level as 3,746 eyes from 1,310 subjects, split into training/validation: 1,987 eyes from 1,180 subjects and testing: 211 eyes from 130 subjects.

The DIGS/ADAGES labels are based on standardized criteria: glaucomatous eyes are identified by repeatable VF defects and/or characteristic ONH structural abnormalities such as rim thinning or localized RNFL loss, while healthy eyes require normal VF results and normal optic disc appearance. These data are used to fine-tune Llama 3.2 Vision-Instruct, an 11-billion-parameter multimodal LLM, with Unsloth, LoRA, QLoRA, 4-bit quantized weights, a frozen vision encoder, and training on one NVIDIA A40 GPU. Each training example pairs an ONH OCT image with the instruction prompt “Describe the OCT scan in detail” and a structured report. If the scan is unusable, the target is the fixed refusal statement: “ONH OCT is unusable due to quality and/or segmentation issues.”

Evaluation covers quality assessment, glaucoma detection, and sector-wise RNFL thinning classification across seven sectors. The reported results are 0.90 accuracy and 0.98 specificity for quality triage; 0.86 accuracy, 0.91 sensitivity, 0.73 specificity, and 0.91 F1-score for glaucoma detection; and RNFL thinning accuracy ranging from 0.83 to 0.94. Text-generation scores are BLEU: 0.82, ROUGE-1: 0.94, ROUGE-2: 0.87, ROUGE-L: 0.92, METEOR: 0.92, and BERTScore-F1: 0.99 (Jalili et al., 1 Oct 2025). In this context, DIGS is not a reconstruction prior or a sampler but a clinically curated source of longitudinal ophthalmic imaging and labels.

6. Additional technical uses: atomic optics, galaxy spectra, and dynamic CBCT

The acronym also appears in several other specialized settings. In atomic optics, a five-level DIGS atom is a dressed-state construction with one excited state $\tau$2, four lower states $\tau$3, one control laser, two RF/microwave fields, and weak incoherent pumping (Sagona-Stophel et al., 2011). The main result is that there exist frequencies with vanishing absorption but nonzero $\tau$4, permitting refractive-index engineering according to

$\tau$5

For Rb vapors on the D1 line, the headline prediction is

$\tau$6

with $\tau$7 in $\tau$8, and the index can also be reduced below 1 by changing the sign of the probe or RF detunings.

In astrophysical inference, DIGS stands for Deep Inference of Galaxy Spectra with Neural Posterior Estimation, a proof-of-concept application of SBI and NPE to simulated noisy galaxy spectra (Khullar et al., 2022). It trains on a dataset of

$\tau$9

generated from a 5-parameter SED model using Prospector, with spectra spanning 3750–9500 Å and represented by 138 flux elements. The reported uncertainty levels are about 0.17 dex in stellar mass and 0.26 dex in metallicity, and the framework conducts rapid SED inference for 0.9–1.2$\Phi(x;\theta_0) \approx \|x\|_2 - r,$0 galaxy spectra at the cost of 1 MCMC-based fit. Here DIGS refers to amortized posterior estimation rather than to geometry or diffusion.

In medical imaging, DIGS also names Dynamic CBCT Reconstruction using Deformation-Informed 4D Gaussian Splatting and a Low-Rank Free-Form Deformation Model (Huang et al., 27 Jun 2025). This framework represents the attenuation field as a sum of Gaussians and applies a single unified deformation vector field $\Phi(x;\theta_0) \approx \|x\|_2 - r,$1 so that

$\Phi(x;\theta_0) \approx \|x\|_2 - r,$2

with covariance updated through the local Jacobian. Motion is modeled by an explicit low-rank FFD basis,

$\Phi(x;\theta_0) \approx \|x\|_2 - r,$3

On six CBCT datasets, the reported mean performance is PSNR: 28.14 dB, RMSE: 1.76, and Time: 15 m 32 s, versus PSNR: 25.86 dB, RMSE: 2.31, and Time: 1 h 40 m for HexPlane. The paper explicitly states that the method is about six times faster than HexPlane. This is again a separate lineage from both divergence-guided implicit surfaces and Diffusive Gibbs Sampling.

Across these usages, the only stable property of “DiGS” is terminological recurrence. Methodologically, the acronym spans neural SDF regularization, Gaussian-splatting geometry, multimodal MCMC, longitudinal ophthalmic cohort design, refractive-index engineering, amortized galaxy-spectrum inference, and dynamic CBCT reconstruction.