Inter-Slice Consistent Stochasticity (ISCS)

• ISCS is a diffusion sampling strategy that replaces independent per-slice Gaussian noise with spatially correlated noise to ensure coherent 3D reconstruction.
• It leverages Slerp-based interpolation between two Gaussian anchors to produce smooth noise variations while preserving slice-wise marginal Gaussianity.
• Empirical results show that ISCS improves metrics like PSNR, SSIM, and LPIPS, outperforming traditional TV regularization in 3D medical imaging tasks.

Searching arXiv for papers on Inter-Slice Consistent Stochasticity and closely related inter-slice consistency methods in 3D medical imaging. arXiv search query: "Inter-Slice Consistent Stochasticity diffusion 3D medical imaging" Inter-Slice Consistent Stochasticity (ISCS) is a sampling-time strategy for 2D diffusion-based 3D medical image reconstruction that enforces smooth, anatomically plausible variation along the slice axis without retraining the diffusion model, adding new loss terms, or introducing additional optimization steps. In the formulation introduced for medical inverse problems, ISCS replaces per-slice independent Gaussian noise with a spatially correlated noise volume generated by spherical linear interpolation (Slerp) between two random anchor noise maps, so that neighboring slices follow aligned sampling trajectories while retaining slice-wise marginal Gaussianity. The method was presented for sparse-view CT, limited-angle CT, and MRI isotropic super-resolution, where stacked 2D diffusion priors otherwise suffer from severe inter-slice discontinuities when applied volume-wise (Du et al., 4 Feb 2026).

1. Problem setting and motivation

ISCS arises in the setting of 3D medical inverse problems of the form

$y = A x + n,$

where $x$ is a 3D volume, $y$ is the measurement, $A$ is the forward operator, and $n$ is noise. The motivating cases include cone-beam sparse-view CT with 30 projection views over $0^\circ$–$360^\circ$, limited-angle CT with 100 views over $[0^\circ,100^\circ]$, and MRI isotropic super-resolution from anisotropic inputs. These problems are especially ill-posed along the $z$-axis, so a reconstruction prior that is only 2D can be locally effective per slice while remaining globally inconsistent across slices (Du et al., 4 Feb 2026).

The immediate practical motivation is the widespread compromise of training diffusion models on 2D slices rather than full 3D volumes. Direct 3D diffusion modeling is difficult because curated volumetric datasets are harder to collect, 3D U-Net-like backbones with 3D convolutions are computationally expensive, memory scales with volume size, and specialized training regimes are often required. As a result, many pipelines apply a pretrained 2D diffusion prior slice by slice and then stack the outputs into a volume. The failure mode is that each slice acquires an independent stochastic trajectory during reverse diffusion, so anatomically corresponding structures can drift, flicker, fragment, or change intensity abruptly when viewed in sagittal or coronal reformats (Du et al., 4 Feb 2026).

Existing remedies often use explicit continuity regularization, typically 3D total variation along $z$. In the paper’s framing, such methods attack the outcome rather than the source of the problem. They require additional optimization, introduce a sensitive hyperparameter, and may over-smooth edges and fine structures such as thin vessels or small lesions. ISCS instead revisits the origin of stochasticity in diffusion sampling and controls the consistency of the stochastic noise components themselves, so that the random trajectories of adjacent slices remain aligned from the start (Du et al., 4 Feb 2026).

2. Diffusion-sampling formulation

The underlying diffusion setup is standard. The forward process is

$x$0

with the closed form

$x$1

where $x$2 and $x$3. A denoiser $x$4 is trained with the usual noise-prediction objective, and the paper uses a VE-style model with an NCSN++ backbone. For inverse problems, the solver alternates denoising prediction, a data-fidelity update, and re-noising (Du et al., 4 Feb 2026).

In a DDIM-like reverse step, the reconstruction update contains a stochastic term:

$x$5

with $x$6. When a 3D volume is reconstructed by processing slices independently, each slice $x$7 receives its own independent $x$8 at every step. In ill-posed regions, these independent perturbations dominate the trajectory, and adjacent slices can converge to different local modes of the learned 2D prior. ISCS modifies precisely this term: the per-slice i.i.d. noise is replaced by a correlated 3D noise volume whose slices remain marginally Gaussian but are strongly correlated for nearby slice indices (Du et al., 4 Feb 2026).

The resulting update is slice-indexed:

$x$9

where $y$0 is no longer independently sampled per slice. The single-slice generative behavior is therefore preserved at the marginal level, while the joint distribution across slices is altered to promote coherence along $y$1 (Du et al., 4 Feb 2026).

3. Slerp-based correlated noise and its geometric rationale

The construction of $y$2 begins by sampling two independent 2D Gaussian anchor maps,

$y$3

for the first and last slices of a volume with $y$4 slices. Their angular separation is

$y$5

and the normalized slice coordinate is

$y$6

ISCS then interpolates geodesically on the hypersphere:

$y$7

This produces a noise field that varies smoothly from slice 1 to slice $y$8, so nearby slices receive similar stochastic forcing while distant slices are less correlated (Du et al., 4 Feb 2026).

The geometric justification is the Gaussian Annulus Theorem. In high dimensions, a draw from $y$9 concentrates near a shell of radius $A$0, so linear interpolation between Gaussian samples traverses low-probability regions, whereas Slerp moves along the geodesic on the typical shell. The paper therefore uses Slerp rather than linear interpolation to preserve norm and approximately preserve the per-slice Gaussian distribution. It further notes that, in high dimensions, the angle between independent Gaussian anchors concentrates near $A$1, which stabilizes the interpolation geometry across runs (Du et al., 4 Feb 2026).

Algorithmically, ISCS is plug-and-play. One identifies the re-noising term in an existing diffusion sampler, batches slices so the current noisy state has a slice dimension, samples two anchors per time step, computes the Slerp-derived $A$2 for each slice, and replaces the standard torch.randn_like-style i.i.d. noise with these correlated maps. Model parameters, training loss, the data-fidelity update, and the diffusion schedule remain unchanged. In the basic form, ISCS introduces no new hyperparameters; the degree of stochasticity is still controlled only by the pre-existing $A$3 or $A$4 schedule (Du et al., 4 Feb 2026).

4. Empirical behavior and comparison with continuity regularization

The reported experiments train the diffusion prior on 2D slices from CT and MRI. For CT, the dataset is the AAPM 2016 low-dose CT challenge with 5410 slices of size $A$5 from 9 patients. For MRI, IXI T1-weighted brain images are used, with a pretrained coronal model from Lee et al. (2023). Evaluation covers CT volumes of roughly $A$6 and MRI volumes padded to $A$7, with anisotropic inputs created by $A$8 downsampling along $A$9. Baselines include FDK and ADMM-TV for CT, cubic upsampling and ADMM-TV for MRI, and diffusion-based DDNM and DDS variants with and without ISCS or TV regularization (Du et al., 4 Feb 2026).

Performance is reported with PSNR, SSIM, LPIPS, and a slice-difference statistic,

$n$0

together with

$n$1

The slice-difference term measures how closely the reconstruction reproduces the ground-truth magnitude of slice-to-slice variation rather than merely enforcing smoothness. In the sparse-view CT setting with 30 views, DDS versus DDS+ISCS changes the axial PSNR from 34.76 to 36.97, axial SSIM from 0.919 to 0.937, axial LPIPS from 0.069 to 0.064, sagittal PSNR from 35.33 to 38.16, sagittal SSIM from 0.904 to 0.942, sagittal LPIPS from 0.141 to 0.065, and the inter-slice difference gap $n$2 from 0.005588 to 0.001835. Similar improvements are reported for limited-angle CT and MRI super-resolution (Du et al., 4 Feb 2026).

A recurrent comparison is with explicit TV-based continuity regularization. The paper states that DDS+ISCS often matches or surpasses DDS+TV in PSNR, SSIM, and LPIPS while preserving fine details better in qualitative examples. The distinction is conceptual as well as numerical: TV acts directly in image space and can blur edge structure, whereas ISCS acts in noise space and correlates the stochastic trajectories without enforcing direct intensity smoothing. The paper also contrasts ISCS with Batch-Consistent Sampling (BCS), which uses identical noise in all slices. BCS is effective in short video sequences but, in 3D medical volumes with substantial anatomical change along $n$3, it produces copying artifacts and over-constrains the sampling. ISCS instead enforces smoothly varying shared randomness rather than identical randomness (Du et al., 4 Feb 2026).

The method is also effective when $n$4, where the reverse process is otherwise deterministic. In that regime, the paper applies the same logic to the initial noise volume $n$5, and reports substantial improvements from correlated initialization alone. Nevertheless, moderate-to-high stochasticity remains beneficial overall, supporting the view that stochastic exploration is useful in ill-posed inverse problems if the stochasticity is structured rather than independent slice by slice (Du et al., 4 Feb 2026).

5. Related formulations and terminological scope

ISCS belongs to a broader line of work concerned with making 2D generative or inverse models behave coherently on 3D volumes. A closely related example is the 2D Brownian Bridge Diffusion Model for slice-consistent 3D brain CT-to-MRI translation, which introduces Style Key Conditioning (SKC) and Inter-Slice Trajectory Alignment (ISTA). That framework removes random sampling at inference, shares a histogram-based style key across all slices, averages predictions from overlapping multi-slice windows, and applies a deterministic score-based correction. A plausible interpretation is that this realizes a deterministic extreme of the same design problem: inter-slice stochasticity is not merely correlated, but effectively collapsed into one coherent volume-level trajectory (Choo et al., 2024).

Another related formulation is PSI3D, which performs plug-and-play 3D stochastic inference with a slice-wise latent diffusion prior and stochastic total variation regularization along the concatenation axis. In that method, each 2D slice is sampled stochastically in latent space, while a TV prior along $n$6 and a split Gibbs sampler couple the slices into a coherent posterior over the full 3D volume. This places the inter-slice-consistency constraint in the prior and MCMC structure rather than in the diffusion re-noising term, but it addresses the same underlying tension between slice-wise stochasticity and volumetric coherence (Guo et al., 20 Dec 2025).

LiFT addresses the same general problem from a feature-space perspective. It factorizes 3D volume synthesis into per-slice image generation and inter-slice trajectory learning, either by mapping a global latent $n$7 into a depth-indexed sequence of conditioning codes in unconditional generation or by using a bidirectional $n$8-context mixer in paired translation. The paper does not use the term ISCS, but it explicitly treats a volume as an ordered trajectory in feature space and constrains that trajectory with a tri-planar drifting loss or a through-plane derivative loss. This suggests a more general view in which inter-slice consistent stochasticity can be implemented not only in noise space, but also in latent trajectory space (Zhang et al., 18 May 2026).

A useful counterpoint is VoxShield, which targets the opposite effect. It introduces an Inter-Slice Frequency Consistency Disruption mechanism that maximizes spectral divergence between adjacent slices in a protected perturbation volume, producing “inter-slice flickering” and “high-frequency spectral jitter along $n$9” to break the volumetric priors of 3D segmentation networks. In that setting, adjacent-slice coherence is deliberately dismantled rather than preserved. This suggests that inter-slice consistency is not merely a perceptual preference; it is an operational prior exploited by volumetric models and can therefore be either reinforced for reconstruction or disrupted for protection (Liu et al., 17 May 2026).

The acronym itself is not stable across fields. In learned image compression, “ISCS” denotes the Invariant Salient Channel Space, a parameter-based organization of latent channels into Salient-Core and Salient-Auxiliary groups for deterministic channel ordering and grouping in VAE-based learned image compression. That work explicitly states that ISCS there is not “Inter-Slice Consistent Stochasticity,” and it contains no explicit notion of inter-slice stochasticity in the medical-imaging sense (Wang et al., 21 Sep 2025).

6. Assumptions, limitations, and extensions

The reported formulation of ISCS assumes a meaningful and consistent slice order along the $0^\circ$0-axis. If slice order is mixed or acquisition ordering is not anatomically coherent, correlating noise across that axis may enforce the wrong continuity pattern. The method also assumes that the noise dimension per slice is high, so the Gaussian geometry underlying Slerp and angle concentration is accurate; typical medical resolutions such as $0^\circ$1 satisfy this condition. A further assumption is that the forward operator $0^\circ$2 and inverse solver are well defined and that the main obstacle is stochastic inconsistency rather than gross model mis-specification (Du et al., 4 Feb 2026).

Several limitations are explicitly noted. Very abrupt anatomical changes between adjacent slices may be biased toward smoother transitions, even though empirical tests on lesion datasets reportedly preserve pathology. Highly anisotropic volumes weaken the meaning of through-plane continuity; robustness is shown for slice spacing between 3 and 7.5 mm, but the paper states that beyond that range performance may depend on the task. ISCS therefore does not remove the need to reason about acquisition geometry and volumetric anisotropy (Du et al., 4 Feb 2026).

The extensions proposed in the original work remain consistent with its central premise. These include learned correlation fields instead of a single Slerp path between two anchors, hybrid 2D–3D approaches that combine ISCS with patch-wise 3D priors or multi-plane priors, and application beyond medical imaging to volumetric microscopy, seismic imaging, or other 3D inverse problems. Taken together with trajectory-based and feature-based approaches in the surrounding literature, this suggests that “inter-slice consistent stochasticity” is best understood not as one fixed algorithm but as a design principle: randomness should be structured across slices so that 3D inference preserves legitimate anatomical variation without collapsing into either independent flicker or globally duplicated slices (Du et al., 4 Feb 2026).