Latent Average Stabilization (LAS)

• Latent Average Stabilization (LAS) is an inference-time Monte Carlo averaging strategy that reduces stochastic variability in conditional generative models for medical imaging.
• It generates multiple latent predictions and averages them before decoding, thereby enhancing spatiotemporal consistency and computational efficiency.
• LAS also estimates uncertainty by measuring latent dispersion, with empirical studies showing improvements in metrics like MSE and SSIM.

Latent Average Stabilization (LAS) is an inference-time Monte Carlo averaging strategy in latent space for stochastic conditional generative models. It was introduced in Brain Latent Progression (BrLP) to stabilize individual-level longitudinal predictions on 3D brain MRIs and was later analyzed in CoCoLIT for MRI-to-PET translation. In both settings, LAS addresses the fact that conditional latent diffusion remains stochastic because reverse diffusion starts from Gaussian noise $z_T \sim \mathcal{N}(0,I)$; repeated forecasts under identical conditioning can therefore differ slightly. LAS counteracts that variability by generating multiple latent predictions, averaging them before decoding, and optionally using their dispersion as an uncertainty estimate (Puglisi et al., 2024, Puglisi et al., 12 Feb 2025, Sargood et al., 2 Aug 2025).

1. Emergence and problem setting

LAS arose in the context of longitudinal neuroimaging, where a model is expected not merely to synthesize a plausible single scan, but to produce a subject-specific trajectory with gradual anatomical change over time. In BrLP, the motivating observation is that different random initial noises can yield slightly different latent outputs even when the same baseline MRI, metadata, and progression covariates are provided. When forecasts are generated across successive timesteps, those stochastic differences can manifest as irregular patterns, non-smooth transitions, or reduced spatiotemporal consistency. LAS was introduced specifically to stabilize this inference procedure and make predicted progression smoother and more consistent with disease evolution (Puglisi et al., 2024, Puglisi et al., 12 Feb 2025).

The later CoCoLIT formulation places LAS in a broader conditional translation setting. There, the method is described as a strategy for turning a stochastic latent generative model into a more stable and efficient estimator of the expected output. Rather than decoding every stochastic sample and averaging in image space, LAS averages in latent space and decodes once. This framing emphasizes both stability and computational efficiency, especially for 3D medical imaging, where decoders are expensive and repeated image-space decoding is costly (Sargood et al., 2 Aug 2025).

A recurrent source of confusion is that LAS is not a training-time regularizer. In BrLP, it is explicitly described as a post-processing or inference-time stabilization strategy. It does not modify the diffusion objective, add a new loss term, enforce a temporal regularizer during training, or update latent averages iteratively during learning. Its role begins only after conditional latent forecasts have been generated (Puglisi et al., 2024, Puglisi et al., 12 Feb 2025).

2. Core algorithm and placement in the generative pipeline

In BrLP, the inference operator is written as

$\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$

where $x^{(A)}$ is the baseline MRI, $c^{(A)}$ is the baseline covariate set, and $z_T \sim \mathcal{N}(0,I)$ is the random initial noise for reverse diffusion. LAS assumes that the single-sample prediction $\hat z^{(B)}$ fluctuates around a theoretical mean

$\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$

Because this expectation is not analytically available, LAS approximates it by repeating the full inference process $m$ times with independent noise draws and averaging: $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$ The final predicted MRI is then decoded from the averaged latent: $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$ Operationally, LAS is therefore “sample $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$0 times, average the latent outputs, decode once” (Puglisi et al., 12 Feb 2025).

Within BrLP, LAS is placed after the full conditional latent generation process and before decoding. The auxiliary model $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$1 first predicts progression-related volumes $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$2 at the target age. These are concatenated with subject-specific metadata $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$3 to form target covariates

$\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$4

The latent diffusion model is conditioned via cross-attention on $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$5, while the ControlNet is conditioned on the baseline subject latent $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$6. LAS does not replace or alter these components; it wraps around them at inference by repeating the stochastic conditional generation $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$7 times, producing $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$8 latent predictions, and averaging them. The method therefore depends on the subject metadata conditioning, the auxiliary disease-progression prior, and the ControlNet-based anatomical conditioning, but it is itself a post hoc stabilizer for the stochastic generative inference procedure (Puglisi et al., 12 Feb 2025).

CoCoLIT uses the same essential construction in a cross-modality setting. If $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$9 is the MRI latent and $x^{(A)}$0 are sampled PET latents from the conditional latent distribution $x^{(A)}$1, LAS forms

$x^{(A)}$2

The algorithmic pattern is unchanged: encode once, generate $x^{(A)}$3 stochastic latent outputs, average them, and decode once (Sargood et al., 2 Aug 2025).

3. Stabilization mechanism and uncertainty estimation

The stabilization effect of LAS in BrLP is attributed to suppression of idiosyncratic noise-induced artifacts. By averaging repeated latent samples, the method biases the prediction toward features that are repeatedly supported across stochastic draws. In longitudinal brain MRI, the target notion of spatiotemporal consistency is that predicted anatomical change should evolve smoothly across ages and should respect the expected progression pattern of the same subject, rather than showing abrupt, unstable, or locally inconsistent changes. The paper explicitly connects LAS to more stable ventricular enlargement, atrophy patterns, and tissue changes over the predicted sequence, instead of flickering or irregular shape changes (Puglisi et al., 12 Feb 2025).

LAS in BrLP also serves as the basis of an uncertainty analysis. After approximating the mean latent prediction $x^{(A)}$4, the model computes a standard deviation over the $x^{(A)}$5 latent samples: $x^{(A)}$6 The components of $x^{(A)}$7 are then averaged into a scalar uncertainty measure $x^{(A)}$8. This is not a voxelwise uncertainty map; it is a global scalar summarizing prediction dispersion in latent space. The interpretation given is that larger latent spread indicates that the model is less certain about the future scan (Puglisi et al., 12 Feb 2025).

The uncertainty signal derived from LAS is reported to be structured rather than arbitrary. In BrLP, uncertainty increases with prediction distance: as the temporal gap between baseline and target age grows, the scalar uncertainty $x^{(A)}$9 rises significantly, with fixed-effect coefficients $c^{(A)}$0 for $c^{(A)}$1 and $c^{(A)}$2 for $c^{(A)}$3, both with $c^{(A)}$4. Higher uncertainty is also associated with worse image quality, with MSE positively correlated with $c^{(A)}$5 ($c^{(A)}$6, $c^{(A)}$7) and SSIM negatively correlated with $c^{(A)}$8 ($c^{(A)}$9, $z_T \sim \mathcal{N}(0,I)$0). The paper interprets this as evidence that the variability measured by LAS is clinically meaningful: when the model is less stable across repeated latent samples, the decoded MRI predictions are less accurate (Puglisi et al., 12 Feb 2025).

4. Empirical behavior in Brain Latent Progression

The original BrLP report introduced LAS as a novel technique to improve spatiotemporal consistency of predicted progression and described it as an inference-time averaging strategy with $z_T \sim \mathcal{N}(0,I)$1. In that version, the full inference process with $z_T \sim \mathcal{N}(0,I)$2 took about $z_T \sim \mathcal{N}(0,I)$3 seconds per MRI on a consumer GPU, and the ablation study reported that LAS reduced volumetric errors by about 5% while modestly improving image similarity. In the same study, the base model without AUX and without LAS had MSE $z_T \sim \mathcal{N}(0,I)$4 and SSIM $z_T \sim \mathcal{N}(0,I)$5, whereas adding LAS gave MSE $z_T \sim \mathcal{N}(0,I)$6 and SSIM $z_T \sim \mathcal{N}(0,I)$7 (Puglisi et al., 2024).

The subsequent BrLP paper expanded the analysis and treated LAS as a tunable Monte Carlo stabilization step. The authors varied $z_T \sim \mathcal{N}(0,I)$8 and reported that most metrics improve as $z_T \sim \mathcal{N}(0,I)$9 increases, with increased computation time as the trade-off. Increasing $\hat z^{(B)}$0 from 2 to 64 reduced MSE by 7%, reduced volumetric errors by 3% on average, and improved SSIM by 0.68%. These improvements were statistically significant for all metrics except the volumetric errors in the amygdala and CSF. On that basis, the main experiments used $\hat z^{(B)}$1 unless stated otherwise (Puglisi et al., 12 Feb 2025).

A direct component ablation isolated the contribution of LAS relative to the auxiliary model. On the internal test set, the base model achieved MSE $\hat z^{(B)}$2 and SSIM $\hat z^{(B)}$3. Adding LAS alone improved these to MSE $\hat z^{(B)}$4 and SSIM $\hat z^{(B)}$5. The combination “Base + LAS + AUX” performed best overall, reaching MSE $\hat z^{(B)}$6, SSIM $\hat z^{(B)}$7, and the lowest volumetric MAEs in most regions, with several results marked significantly better than all alternatives. The authors summarize the contribution of LAS as an additional 4% reduction in volumetric errors beyond the auxiliary model, with LAS and AUX together yielding a 21% reduction (Puglisi et al., 12 Feb 2025).

These results establish a specific empirical profile. LAS improves performance over a single stochastic forecast, but its benefit depends on the number of repeated samples $\hat z^{(B)}$8. The effect is most naturally interpreted as a variance-reduction mechanism for stochastic conditional generation. A plausible implication is that LAS is especially useful when the latent diffusion model is already well conditioned but still exhibits nuisance variability across repeated runs.

5. Theoretical analysis and extension in CoCoLIT

CoCoLIT extends LAS from longitudinal MRI forecasting to MRI-to-PET synthesis and adds an explicit theoretical analysis. The paper compares LAS with the unbiased estimator that averages decoded outputs: $\hat z^{(B)}$9 whereas LAS uses

$\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$0

The computational motivation is immediate: the unbiased estimator requires decoding all sampled outputs, while LAS performs only one decoder pass after latent averaging (Sargood et al., 2 Aug 2025).

The central theoretical result in CoCoLIT is that LAS is asymptotically biased as an estimator of the expected decoded output. Let

$\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$1

be the conditional latent mean and let $\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$2 denote the latent covariance. A second-order Taylor expansion of the decoder yields

$\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$3

while for LAS,

$\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$4

The approximate bias is therefore

$\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$5

and as $\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$6,

$\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$7

The formal conclusion is therefore not that LAS is unbiased, but that its bias can be negligible when the conditional latent distribution is concentrated and the decoder is locally close to linear in the relevant region (Sargood et al., 2 Aug 2025).

CoCoLIT empirically tests that local-linearity condition with latent interpolation experiments. For sampled latent pairs, the paper reports a mean Pearson correlation coefficient of $\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$8 in the distance-linearity test and a mean MSE of $\mu^{(B)} = \mathbb{E}\big[\hat z^{(B)}\big].$9 in the straightness test. These results are used to support the claim that the decoder is locally close to linear in the sampled latent regions, making LAS’s bias practically small in that application (Sargood et al., 2 Aug 2025).

The empirical ablations in CoCoLIT also reinforce the practical value of LAS. With $m$0, internal test set metrics improve monotonically or near-monotonically. Selected values were $m$1: SSIM $m$2, PSNR $m$3, MSE $m$4, BA $m$5; $m$6: SSIM $m$7, PSNR $m$8, MSE $m$9, BA $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$0; $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$1: SSIM $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$2, PSNR $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$3, MSE $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$4, BA $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$5; and $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$6: SSIM $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$7, PSNR $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$8, MSE $$\mu^{(B)} = \mathop{\mathbb{E}_{z_T \sim \mathcal{N}(0,I)} \bigg[ \mathcal{I}(z_T, x^{(A)}, c^{(A)})\bigg]} \approx \frac{1}{m}\sum^m \mathcal{I}(z_T, x^{(A)}, c^{(A)}).$$9, BA $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$0. The paper selected $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$1 as the default. In a direct comparison between LAS and the unbiased image-space average at $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$2, the two estimators were nearly identical in practical performance: the unbiased estimator had SSIM $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$3, PSNR $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$4, MSE $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$5, CABC $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$6, HABC $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$7, BA $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$8, while LAS had SSIM $\hat x^{(B)} = \mathcal{D}(\mu^{(B)}).$9, PSNR $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$00, MSE $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$01, CABC $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$02, HABC $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$03, BA $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$04 (Sargood et al., 2 Aug 2025).

6. Limitations, scope, and acronym disambiguation

Several limitations recur across the BrLP and CoCoLIT accounts. First, LAS increases inference cost linearly with $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$05; this creates an explicit accuracy–runtime trade-off. BrLP mitigates this by parallelizing generation of multiple latent samples on a single GPU and by using DDIM sampling with 25 denoising steps at inference, while CoCoLIT also emphasizes that decoder cost is reduced but latent generation for $\hat z^{(B)} = \mathcal{I}(z_T, x^{(A)}, c^{(A)}),$06 samples remains necessary (Puglisi et al., 12 Feb 2025, Sargood et al., 2 Aug 2025).

Second, LAS assumes that repeated stochastic diffusion samples are centered around a meaningful latent expectation and that averaging them is beneficial rather than harmful. In BrLP, this is treated as reasonable because the stochasticity of reverse diffusion is viewed as nuisance variability, not as desired multimodal uncertainty. In CoCoLIT, the same point is recast through decoder curvature and latent covariance: LAS works best when the latent distribution is sufficiently concentrated and the decoder is locally close to linear (Puglisi et al., 12 Feb 2025, Sargood et al., 2 Aug 2025).

Third, LAS does not enforce a hard temporal constraint. The earlier BrLP account notes limitations in underrepresented conditions, such as ages over 90 years, where the method can produce slightly non-monotonic progression. This indicates that averaging stochastic outputs can reduce randomness without guaranteeing true physiological monotonicity, especially when the model is extrapolating outside the training distribution (Puglisi et al., 2024).

The acronym itself is overloaded across multiple research areas. In large-MIMO detection, LAS denotes “likelihood ascent search,” a family of local-search detectors for ML-like symbol detection rather than latent-space averaging (0806.2533, Jr et al., 2014, Sun, 2024). In spiking LLMs, LAS denotes “Loss-less ANN-SNN Conversion,” a training-free conversion framework built around Outlier-Aware Threshold and Hierarchically Gated neurons (Chen et al., 14 May 2025). These are distinct uses of the same acronym. Within medical latent generative modeling, however, “Latent Average Stabilization” refers specifically to inference-time averaging of repeated latent samples, decoding of the averaged latent, and, in BrLP, extraction of a scalar uncertainty measure from latent dispersion (Puglisi et al., 12 Feb 2025, Sargood et al., 2 Aug 2025).