Spatiotemporal Disaggregation Overview

• Spatiotemporal disaggregation is the process of estimating fine-resolution data from coarsely aggregated observations using explicit change-of-support techniques.
• It employs diverse methodologies, including Bayesian models, deep generative networks, and constrained optimization, to enforce spatial-temporal coherence and propagate uncertainty.
• Applications span from generating detailed mobility trajectories and refining economic indicators to enhancing environmental risk assessments.

Spatiotemporal disaggregation denotes the recovery, generation, or estimation of fine-resolution quantities over space and time from observations available only after aggregation, coarsening, or structural compression. Across recent work, the term covers several distinct but related tasks: generating full mobility trajectories from aggregate spatial occupancy heatmaps; allocating coarse areal counts or proportions to finer spatial and temporal supports; reconstructing regional time series from aggregate national series while modeling spatial spillovers; and decomposing spatially indexed time series into contiguous regions and representative temporal signatures (Bergström et al., 2024, Han et al., 2023, Benedetti et al., 2021, Ripstein et al., 23 Jun 2026, Tobar et al., 4 Sep 2025, Avellaneda et al., 9 Nov 2025, Weng et al., 6 May 2026). The common technical core is a change-of-support problem: a latent fine-scale process must be linked coherently to observed coarse spatial units, temporal windows, or non-temporal marginals, while preserving uncertainty quantification and, in many settings, benchmarking constraints.

1. Conceptual scope and problem classes

The literature does not use spatiotemporal disaggregation in a single uniform sense. In mobility generation, it means sampling detailed trajectories $x$ from aggregate, non-temporal spatial statistics $l$, with the conditional target written as $p(x \mid l)$ and the joint factorized as $p(x,l)=p(x\mid l)p(l)$ (Bergström et al., 2024). In areal prediction, it denotes inference on latent annual tract-level proportions or fine-scale risk surfaces from multi-year or polygon-aggregated observations, typically through explicit aggregation operators on the probability or intensity scale (Benedetti et al., 2021, Ripstein et al., 23 Jun 2026, Avellaneda et al., 9 Nov 2025). In spatial econometrics, it means reconstructing region-level time series from an observed aggregate series under spatial autoregression, temporal dependence, and exact coherence constraints (Tobar et al., 4 Sep 2025). In structurally constrained neural modeling, it means mapping low-resolution irregular partitions to high-resolution irregular partitions while respecting containment relations (Han et al., 2023). A broader, information-theoretic interpretation treats it as a decomposition of spatial time series into contiguous regions and regional drivers that minimize description length (Weng et al., 6 May 2026).

These formulations differ in what is observed, what is latent, and how coherence is enforced.

Formulation	Observed support	Fine-scale target
Conditional mobility generation	Spatial occupancy heatmap $l$	Trajectories $x$ (Bergström et al., 2024)
Irregular areal downscaling	Coarse partition $C$ or multi-year estimates	Fine partition $F$ or annual tract values (Han et al., 2023, Benedetti et al., 2021)
Aggregated point-process inference	Counts over polygons $A_{i,t}$	Risk or intensity surface over $M$ (Ripstein et al., 23 Jun 2026)
Aggregate time-series reconstruction	Aggregate series $l$0	Region-level series $l$1 (Tobar et al., 4 Sep 2025)
Continuous footprint/window averaging	Averaged observations over $l$2	Continuous field $l$3 (Avellaneda et al., 9 Nov 2025)
Structured regional decomposition	Spatially indexed time series	Contiguous regions and drivers (Weng et al., 6 May 2026)

Taken together, these formulations suggest that the central object is not any specific model class, but the mapping between coarse and fine supports under explicit spatial and temporal structure.

2. Core mathematical structure: change of support, coherence, and conditioning

A defining feature of spatiotemporal disaggregation is the explicit representation of how fine-scale latent quantities aggregate to observed data. In hierarchical areal disaggregation, SARN defines coarse regions $l$4, fine regions $l$5, time index $l$6, and a binary containment matrix $l$7 with the coherence requirement

$l$8

for each coarse region $l$9 and time $p(x \mid l)$0 (Han et al., 2023). In survey-based disaggregation, annual latent proportions $p(x \mid l)$1 are aggregated to areal, multi-year proportions by denominator weights $p(x \mid l)$2,

$p(x \mid l)$3

while the American Community Survey application uses a five-year average on the probability scale for tract estimates and household-weighting for one-year PUMA estimates (Benedetti et al., 2021). In spatial econometric disaggregation, exact benchmarking is written compactly as

$p(x \mid l)$4

with $p(x \mid l)$5, so the latent regional series must sum to the known aggregate at every time point (Tobar et al., 4 Sep 2025).

For point-process or continuous latent-field models, the change of support is expressed by integrals. Under changing areal boundaries, the aggregated log-Gaussian Cox process uses

$p(x \mid l)$6

so each polygon-time count is linked to a shared latent spatial field through a time-varying aggregation operator (Ripstein et al., 23 Jun 2026). In diffusion-SPDE disaggregation, observations are averages over spatial footprints and time windows,

$p(x \mid l)$7

with $p(x \mid l)$8 obtained by integrating the latent Gaussian random field over $p(x \mid l)$9 (Avellaneda et al., 9 Nov 2025).

Conditional generative formulations differ from hard benchmarking formulations. TDDPM does not add an explicit constraint loss; instead, it learns

$p(x,l)=p(x\mid l)p(l)$0

so aggregate alignment emerges from conditioning on heatmap tokens at each denoising step rather than from exact conservation constraints (Bergström et al., 2024). STPN occupies an intermediate position: its symbolic predictions are refined by a convex quadratic program with exact summation and nonnegativity constraints,

$p(x,l)=p(x\mid l)p(l)$1

which restores physical consistency in residential electric energy disaggregation (Jiang et al., 2017).

A common misconception is that spatiotemporal disaggregation always enforces exact benchmarking. The literature shows three regimes: exact coherence by construction or constrained projection (Han et al., 2023, Tobar et al., 4 Sep 2025, Jiang et al., 2017); probabilistic change-of-support with uncertainty propagation (Benedetti et al., 2021, Ripstein et al., 23 Jun 2026, Avellaneda et al., 9 Nov 2025); and conditional generative alignment without explicit constraint terms (Bergström et al., 2024).

3. Methodological families

Deep generative models treat disaggregation as conditional synthesis. TDDPM is a denoising diffusion model with a transformer encoder as the denoiser, operating in unconditional and conditional modes. The conditional prior $p(x,l)=p(x\mid l)p(l)$2 is a local spatial occupancy frequency heatmap split into $p(x,l)=p(x\mid l)p(l)$3 patches, yielding $p(x,l)=p(x\mid l)p(l)$4 heatmap tokens. Conditioning is realized through token concatenation and transformer self-attention, with no classifier-free guidance, $p(x,l)=p(x\mid l)p(l)$5-prediction, or cross-attention module (Bergström et al., 2024). This design makes spatiotemporal disaggregation a full-sequence, non-autoregressive generation problem, and it also supports counterfactual conditioning through modified heatmaps for blocked or added roads.

Neural disaggregation over irregular partitions emphasizes hierarchy-aware coherence. SARN integrates Structurally-Aware Spatial Attention (SASA) with a Gated Recurrent Unit. SASA combines global attention, which captures long-range interactions across regions and levels, with structural attention masked by the containment matrix $p(x,l)=p(x\mid l)p(l)$6, ensuring parent-child message passing only along valid hierarchical relations (Han et al., 2023). The temporal component is handled by a GRU, so spatial context and temporal memory are learned jointly. The paper also explores transfer learning, reporting fine-tuning from one city variable to another using only a few hundred samples (Han et al., 2023).

Symbolic probabilistic models frame disaggregation as inference over symbolic dynamics and directed dependencies. STPN begins by symbolizing continuous time series, constructing a probabilistic finite-state automaton for each subsystem and cross-state transition matrices for directed relational patterns. Directed mutual information,

$p(x,l)=p(x\mid l)p(l)$7

quantifies predictive dependency from subsystem $p(x,l)=p(x\mid l)p(l)$8 to subsystem $p(x,l)=p(x\mid l)p(l)$9 (Jiang et al., 2017). In the residential demand-side setting, whole-building electric consumption is decomposed into HVAC, LIGHTS, APPL, and MELS, and a convex consistency correction imposes exact summation and nonnegativity.

Bayesian disaggregation models treat fine-scale quantities as latent stochastic processes observed through aggregate measurements. The ACS framework converts published design-based variances into effective sample sizes and effective numbers of cases,

$l$0

and then uses a Binomial working likelihood while aggregating on the probability scale (Benedetti et al., 2021). The latent annual tract-level proportions are modeled through a probit link to a spatiotemporal Gaussian process approximated by ST-MRA. Under changing areal boundaries, the DAST framework extends the spatially aggregated log-Gaussian Cox process, replaces polygon-time lognormal effects with gamma-distributed overdispersion, and obtains a marginal negative binomial likelihood within the Extended Latent Gaussian Model framework (Ripstein et al., 23 Jun 2026). In AOD nowcasting, a diffusion-SPDE latent Gaussian field is linked to coarse footprint/window averages through an aggregation matrix $l$1, and inference is performed with INLA-SPDE (Avellaneda et al., 9 Nov 2025).

Spatial econometric models cast disaggregation as constrained prediction under space-time covariance. The spatial disaggregation of time series paper specifies a SAR model with AR(1) region-specific errors,

$l$2

and then derives a constrained BLUP that enforces aggregation and optional anchoring constraints (Tobar et al., 4 Sep 2025). This directly extends classical temporal disaggregation by embedding spatial spillovers in the covariance structure.

Finally, an information-theoretic line of work treats disaggregation as structured partitioning. The MDL-based regionalization framework encodes a spatial partition, region-level drivers, contingency tables, and conditional member series, minimizing a total description length

$l$3

while enforcing spatial contiguity by construction (Weng et al., 6 May 2026). This suggests a broader view in which disaggregation can mean decomposition of space-time data into contiguous, compressive components rather than only allocation from a known aggregate.

4. Inference, conditioning, and computational scaling

Inference strategies in this literature are tightly coupled to the aggregation operator. Bayesian models based on change-of-support typically rely on approximate latent Gaussian inference. The ACS model uses MCMC with Gibbs and Metropolis–Hastings, Albert–Chib augmentation for the probit-binomial link, and ST-MRA dimension reduction, with convergence assessed by trace plots and Geweke diagnostics and post-burn-in effective sample size exceeding $l$4 for each parameter (Benedetti et al., 2021). The changing-boundary LGCP instead uses ELGM with automatic differentiation via TMB, inner trust-region optimization, outer optimization over hyperparameters, and adaptive Gauss–Hermite quadrature; the gamma–negative-binomial construction removes one latent variable per polygon-time pair and is reported to fit datasets with thousands of polygon-time pairs in minutes rather than days required by bespoke MCMC for aggregated LGCPs (Ripstein et al., 23 Jun 2026). The diffusion-SPDE model uses the SPDE–GMRF representation, sparse precision matrices, and R-INLA/INLAspacetime, with the aggregation matrix $l$5 having non-negative rows that sum to one (Avellaneda et al., 9 Nov 2025).

Neural models address scalability differently. TDDPM uses a single transformer encoder, tokenizes the spatial prior into $l$6 heatmap patches, and performs full-sequence denoising. Empirically, it is reported to train up to $l$7 faster than GAN-based SOTA, $l$8 faster than VAE-based SOTA, and $l$9 faster than DiffusionTS; sampling is $x$0 faster than DiffusionTS, and drawing $x$1 samples takes approximately $x$2 minutes (Bergström et al., 2024). SARN’s stated complexities separate dense global attention, $x$3 per time step, from masked structural attention, $x$4, and GRU updates, $x$5 (Han et al., 2023). STPN learns transitions in $x$6 per node or edge, yielding $x$7 for all directed edges, while the convex refinement is a small equality-constrained quadratic program (Jiang et al., 2017). The MDL regionalization algorithm maintains admissible merges in a binary heap and achieves

$x$8

runtime, with a near-linear empirical slope in log runtime versus $x$9 (Weng et al., 6 May 2026).

The handling of conditioning also varies sharply. TDDPM conditions directly through self-attention over concatenated tokens and does not tune guidance scales (Bergström et al., 2024). SARN encodes cross-level structure through hard masking by $C$0 and, optionally, a hierarchical coherence loss (Han et al., 2023). Spatial econometric disaggregation conditions through linear restrictions, with anchoring implemented by augmenting the constraint matrix and applying the same constrained BLUP formula (Tobar et al., 4 Sep 2025). Bayesian areal models condition implicitly through likelihood terms defined on multiple supports, such as one-year PUMA and five-year tract ACS estimates jointly (Benedetti et al., 2021).

5. Evaluation protocols and empirical domains

Evaluation reflects the diversity of targets. In generative mobility, TDDPM introduces a benchmark spanning sequence lengths from $C$1 to $C$2, evaluates distributional fidelity with TimeFID, downstream utility with TSTR, and spatial aggregate alignment with KL divergence, symmetric KL, and Jensen–Shannon divergence between real and synthetic heatmap histograms (Bergström et al., 2024). The paper reports that, for GeoLife length $C$3, conditional TDDPM trained on one quadrant achieves $C$4 and $C$5 over the full area, outperforming unconditional TDDPM and all baselines (Bergström et al., 2024). SARN reports improvements over other neural models of $C$6 and $C$7, and over heuristic methods of $C$8 and $C$9, across two mobility datasets (Han et al., 2023).

In energy and NILM settings, STPN evaluates both supply-side forecasting and demand-side disaggregation. For wind turbine prediction, the reported continuous power prediction error is $F$0 versus $F$1 (Jiang et al., 2017). For NILM in April, the paper reports

$F$2

and notes that STPN+convex programming reduces end-use prediction differences to less than $F$3 relative to the summed WBE (Jiang et al., 2017).

Survey-based and disease-mapping applications emphasize calibration and coverage. In the ACS poverty application, out-of-sample prediction on three-year county-level ACS estimates yields $F$4, $F$5, and coverage of approximately $F$6 for $F$7 posterior intervals and $F$8 for $F$9 posterior intervals under the proposed model (Benedetti et al., 2021). The changing-boundary mortality model is illustrated on NUTS-3 mortality in Belgium and the Netherlands from 2018 to 2023 and reports a high-risk area near Antwerp at roughly $A_{i,t}$0 above average with about $A_{i,t}$1 confidence of elevated risk (Ripstein et al., 23 Jun 2026).

Economic and atmospheric disaggregation use both predictive accuracy and substantive plausibility. In Spanish GDP disaggregation, Gower-based spatial weights with anchoring yield $A_{i,t}$2 and relative RMSE $A_{i,t}$3, improving on contiguity weights and non-anchored variants (Tobar et al., 4 Sep 2025). In the India AOD study, the model improves spatial resolution from $A_{i,t}$4 to $A_{i,t}$5 and temporal resolution from $A_{i,t}$6 hours to $A_{i,t}$7 hour; at the Delhi grid cell, hourly disaggregated predictions interpolate the $A_{i,t}$8-hourly observed averages while preserving coarse-scale features and adding fine-scale temporal detail (Avellaneda et al., 9 Nov 2025).

The MDL regionalization framework evaluates recovered structure by Adjusted Mutual Information and inverse compression ratio $A_{i,t}$9, showing high AMI at low noise in synthetic settings, $M$0 and $M$1 for California AQI, and a China-wide NDVI application with approximately $M$2 sites, $M$3, and runtime of approximately $M$4 minutes in pure Python (Weng et al., 6 May 2026). Although this is not a benchmarking framework in the narrow allocation sense, it provides a quantitative view of how much coarse spatiotemporal structure can be extracted from large datasets.

These studies collectively show that evaluation is not standardized across subfields. Some frameworks prioritize exact aggregate recovery, some prioritize fidelity of generated trajectories, some prioritize calibrated uncertainty, and some prioritize compressive explanatory structure.

6. Assumptions, misconceptions, and active directions

Spatiotemporal disaggregation is often mistaken for spatial interpolation plus temporal smoothing. The current literature shows a more heterogeneous set of assumptions. TDDPM assumes that aggregate priors as heatmaps adequately summarize local spatial usage and notes that temporal variability is not explicitly modeled in $M$5; it also omits road-graph topology and simplifies irregular sampling by constant time steps (Bergström et al., 2024). SARN relies on accurate containment relations $M$6 and can oversmooth when fine-level ground truth is unavailable and training depends mainly on coherence and auxiliary features (Han et al., 2023). STPN assumes approximate stationarity and a first-order Markov property for symbol dynamics, and it can degrade when end-uses have highly overlapping symbol distributions or weak mutual information with whole-building consumption (Jiang et al., 2017). The ACS model assumes conditional independence of one-year PUMA and five-year tract estimates given latent proportions, separable space-time covariance, and correct design-based variances for effective sample size construction (Benedetti et al., 2021). The changing-boundary LGCP uses a shared latent spatial field $M$7 across time rather than an explicit $M$8, leaving temporally evolving latent fields as future work (Ripstein et al., 23 Jun 2026). The GDP framework warns that estimates become unstable when $M$9 approaches unity without strong covariate signal (Tobar et al., 4 Sep 2025). The diffusion-SPDE AOD model requires careful mesh design and buffering to avoid boundary artifacts and does not remove the fundamental identifiability limit that fine-scale features unsupported by the data cannot be recovered (Avellaneda et al., 9 Nov 2025). The MDL framework assumes a static partition over the observed period and does not model time-varying boundaries or lagged cross-region dependence (Weng et al., 6 May 2026).

Another misconception is that more flexible models automatically provide better disaggregation. Several papers instead emphasize calibrated regularization. The ACS work shows that accounting for design effects via ESS and ENC yields better calibration, especially as design effect increases (Benedetti et al., 2021). The changing-boundary mortality paper uses Penalized Complexity priors that prefer smooth, low-variance spatial surfaces and shrink the negative binomial dispersion toward the Poisson model (Ripstein et al., 23 Jun 2026). The GDP paper shows that anchoring partial observations can substantially reduce prediction variance (Tobar et al., 4 Sep 2025). This suggests that identifiability in disaggregation is often driven less by raw model capacity than by well-specified aggregation operators, appropriate priors or constraints, and informative auxiliary structure.

Current directions in the literature point toward richer conditioning and more adaptive supports. TDDPM already supports what-if analysis by modifying aggregate heatmaps without retraining (Bergström et al., 2024). SARN indicates transfer learning across variables with only a few hundred samples (Han et al., 2023). The DAST framework explicitly addresses changing boundaries (Ripstein et al., 23 Jun 2026). The diffusion-SPDE work points to multi-source, multi-resolution fusion and non-Gaussian likelihoods (Avellaneda et al., 9 Nov 2025). The MDL framework identifies time-varying partitions and hybrid covariate-informed coding as extensions (Weng et al., 6 May 2026). A plausible implication is that future work will increasingly combine exact change-of-support operators, uncertainty-aware latent-process models, and flexible conditional generative mechanisms rather than treating these as disjoint traditions.