A Generative Framework for the Creation of Multi-Attribute Geographically-Explicit Synthetic Population

Technical Summary: A Generative Framework for the Creation of Multi-Attribute Geographically-Explicit Synthetic Population

Problem Statement
The creation of multi-attribute synthetic populations is foundational for geo-simulation techniques, including micro-simulation and agent-based modeling. However, existing methods face significant challenges in reconstructing region-specific joint distributions of individual attributes using only aggregated-level data (e.g., census tract-level statistics). Aggregated data records marginal distributions but lacks information on how attributes co-occur at the individual level. Consequently, traditional methods like Iterative Proportional Fitting (IPF) or Hierarchical Sampling often rely on fixed heuristics or probabilistic structures that fail to capture spatial non-stationarity. This leads to internal demographic biases (e.g., unrealistic age-income-education combinations) and a loss of population heterogeneity, particularly in regions with distinct demographic profiles. Furthermore, while combinatorial optimization (CO) methods can preserve region-specific distributions using individual-level data, they are computationally expensive, region-specific, and lack generalizability across different geographic areas.

Methodology
The authors propose a hierarchical diffusion-based generative framework designed to create a nationwide, geographically-explicit synthetic population for the United States (50 states and Washington, D.C.). The framework operates in three primary steps:

1. Data Preparation and Vector Construction:

   • Training Targets ($p$): Individual-level data from the 2023 American Community Survey (ACS) Public Use Microdata Sample (PUMS) covering 2,462 Public Use Microdata Areas (PUMAs) are used to construct the training target. This involves mapping PUMS variables to categorical bins defined in aggregated ACS tables to create a 3,000-dimensional vector representing the true region-specific joint distribution of five attributes: age, gender, education, employment, and income.
   • Condition Vectors ($c$ and $h$): Aggregated-level census data (ACS Detailed Tables) are converted into probability distributions to form condition vector $c$, representing marginal distributions. Additionally, spatial data (POI and LODES commuting flows) are aggregated and encoded into a spatial representation vector $h$ to capture functional characteristics and preserve spatial non-stationarity.

2. Hierarchical Generative Process (Diffusion Model):
   To address the complexity of predicting a 3,000-dimensional joint distribution in a single stage, the framework employs a two-stage diffusion process:

   • Stage 1 (Coarse Generation): A diffusion model predicts a coarse joint distribution ($\hat{p}_{coarse}$) using the condition vectors $c$ and $h$. The target space is reduced from 3,000 fine-grained combinations to 960 coarse combinations by grouping adjacent or substantively similar categories (e.g., compressing age groups). This stage learns the broad demographic structure while preserving spatial variations.
   • Stage 2 (Fine-Grained Refinement): A second diffusion model refines the coarse predictions into the full 3,000-dimensional joint distribution ($\hat{p}$). It takes the coarse group $g$ and its predicted probability as input, then predicts the conditional probability distribution ($\hat{p}^{inner}_{k|g}$) for the fine-grained combinations within that group. The final probability for any specific combination $k$ is calculated as the product of the coarse probability and the inner-coarse refinement probability.

3. Synthetic Individual Generation and Location Assignment:

   • Sampling: Synthetic individuals are sampled from the predicted full joint distribution $\hat{p}$ for each PUMA.
   • Home Location: Individuals are allocated to specific census tracts within a PUMA using an iterative proportional fitting process constrained by the predicted joint distribution and the marginal distributions of age and gender from ACS tract-level data. Explicit home coordinates (latitude/longitude) are assigned along the residential road network, spaced approximately 50 meters apart.
   • Work Location: Employed individuals are assigned work tracts based on LODES commuting flow probabilities from their home tract. Explicit workplace coordinates are assigned along secondary roads and intersections.

Key Contributions

• Hierarchical Diffusion Framework: The paper introduces a novel two-stage diffusion architecture that successfully reconstructs complex, high-dimensional joint distributions of five attributes while preserving spatial non-stationarity, overcoming the limitations of single-stage models and fixed-heuristic methods.
• Geographically-Explicit Population: The framework generates a synthetic population of 332,387,543 individuals across 2,462 PUMAs, complete with explicit home and work locations, rather than just attribute distributions.
• Scalability and Generalizability: Unlike combinatorial optimization methods that are region-specific, this framework utilizes a trained model to generate populations for regions excluded from the training set, demonstrating transferability across the entire nation.

Results and Validation
The framework was validated through internal consistency checks and a held-out regional experiment (excluding Michigan):

• Joint Distribution Reconstruction: The generated populations achieved a mean Total Variation Distance (TVD) of 0.116 against the target PUMS joint distributions, representing an 88.4% overlap.
• Marginal Consistency: The synthetic population preserved marginal distributions with low average absolute differences (AAD) compared to aggregated census data (e.g., 0.0012 for age, 0.0009 for gender).
• Comparison with Baselines: In the held-out experiment, the proposed framework outperformed Iterative Proportional Fitting (IPF), Combinatorial Optimization (CO), and a one-stage Diffusion Probabilistic Model (DDPM). The proposed method achieved a mean TVD of 0.119, representing a 6.3% improvement over IPF and CO, and a 19.1% improvement over the one-stage DDPM baseline.
• Attribute Co-occurrence: Pairwise decomposition analysis showed the framework significantly improved the reconstruction of attribute combinations not explicitly recorded in aggregate data (e.g., education–income, age–income), indicating an ability to infer latent socioeconomic dependencies.

Significance and Claims
The authors claim that this framework provides a scalable and generalized approach for creating multi-attribute, geographically-explicit synthetic populations at both regional and national levels. By reconstructing region-specific joint distributions with high fidelity, the resulting synthetic population introduces more realistic behaviors into geo-simulations, such as agent-based modeling. This capability enables further exploration of the emergence of complex urban phenomena driven by human interactions. The work addresses the critical gap between aggregated census data and the need for realistic, individual-level synthetic data that respects spatial heterogeneity.

Limitations and Future Work
The authors acknowledge several limitations:

• Age Granularity: The use of PUMA-level constraints results in age groups rather than exact ages, particularly for the broad 5–17 age range.
• Daytime Locations: The current framework does not assign daytime locations (e.g., schools) for individuals under 18, as LODES data only covers employed adults.
• Spatial Assignment: The precision of home and workplace location assignment is limited by the available spatial data (road networks, POIs, commuting flows). Future work aims to incorporate finer-grained signals to strengthen spatial assignment.

Data and Code Availability
The resulting datasets (organized by state in .csv format) are available on OSF, and all processing, training, and validation scripts are available on GitHub.