cs.CVApr 14, 2026

Conflated Inverse Modeling to Generate Diverse and Temperature-Change Inducing Urban Vegetation Patterns

Authors: Baris Sarper Tezcan, Hrishikesh Viswanath, Rubab Saher, Daniel Aliaga

Organizations: Computer Science Purdue University, West Lafayette, IN, USA · Forestry and Natural Resources Purdue University, West Lafayette, IN, USA

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Abstract

Urban areas are increasingly vulnerable to thermal extremes driven by rapid urbanization and climate change. Traditionally, thermal extremes have been monitored using Earth-observing satellites and numerical modeling frameworks. For example, land surface temperature derived from Landsat or Sentinel imagery is commonly used to characterize surface heating patterns. These approaches operate as forward models, translating radiative observations or modeled boundary conditions into estimates of surface thermal states. While forward models can predict land surface temperature from vegetation and urban form, the inverse problem of determining spatial vegetation configurations that achieve a desired regional temperature shift remains largely unexplored. This task is inherently underdetermined, as multiple spatial vegetation patterns can yield similar aggregated temperature responses. Conventional regression and deterministic neural networks fail to capture this ambiguity and often produce averaged solutions, particularly under data-scarce conditions. We propose a conflated inverse modeling framework that combines a predictive forward model with a diffusion-based generative inverse model to produce diverse, physically plausible image-based vegetation patterns conditioned on specific temperature goals. Our framework maintains control over thermal outcomes while enabling diverse spatial vegetation configurations, even when such combinations are absent from training data. Altogether, this work introduces a controllable inverse modeling approach for urban climate adaptation that accounts for the inherent diversity of the problem. Code is available at the GitHub repository.

Figures & tables

Figure 1: Our conflated framework combines a predictive forward model with a diffusion-based generative inverse model to produce diverse, physically plausible image-based vegetation patterns conditioned on specific temperature goals (left pair temperature decrease and right pair temperature increase). Higher NDVI values (closer to 1) indicate denser vegetation, while lower NDVI values indicate sparser vegetation.
Figure 2: We show our system pipeline, including inverse and forward model, and the training and inference processes.
Figure 3: Diversity. Diverse NDVI generation under identical conditioning ( Δ\Delta = 0) for two representative cities (Chicago and Overland Park); images demonstrate consistent diversity across distinct urban morphologies while preserving context outside the ROI. Higher NDVI values (closer to 1) indicate denser vegetation, while lower NDVI values indicate sparser vegetation.
Figure 4: Chicago Specificity. Images show the ability to alter regional temperature to specific changes in a Chicago tile. Top: generated NDVI for Δtarget∈{−2,−1,0,+1,+2}∘\Delta_{\text{target}}\in\{-2,-1,0,+1,+2\}^{\circ} C. Bottom: forward-model predicted LST. Numbers indicate ROI mean Δpred\Delta_{\text{pred}} .
Figure 5: Overland Park Specificity. Images show the ability to alter regional temperature to specific changes in an Overland Park tile. Top: generated NDVI for Δtarget∈{−2,−1,0,+1,+2}∘\Delta_{\text{target}}\in\{-2,-1,0,+1,+2\}^{\circ} C. Bottom: forward-model predicted LST. Numbers indicate ROI mean Δpred\Delta_{\text{pred}} .
λ\lambdaBest wwCtrlErr avg{}_{\text{avg}}BaseErr ROI{}_{\text{ROI}} (Δ=0)(\Delta=0)Diversity
150.772±0.3500.772\pm 0.3501.490.707±0.2280.707\pm 0.228
230.715±0.3010.715\pm 0.3011.510.830±0.1180.830\pm 0.118
430.637±0.2300.637\pm 0.2301.530.879±0.0700.879\pm 0.070
630.609±0.2510.609\pm 0.2511.550.888±0.0640.888\pm 0.064
830.573±0.2570.573\pm 0.2571.590.889±0.0620.889\pm 0.062
1630.559±0.3100.559\pm 0.3101.630.905±0.0520.905\pm 0.052
Table 1: Training. Results at ROI scale ( k=32k=32 ) and for various values for λ\lambda . For each configuration, we report the best temperature control error (CtrlErr avg{}_{\text{avg}} ) over w∈{1,2,3,5,8}w\in\{1,2,3,5,8\} . BaseErr ROI{}_{\text{ROI}} ( Δ\Delta = 0) denotes the absolute difference between the predicted and ground-truth mean ROI temperature for samples generated with Δ\Delta = 0.
ModelLST CoarsePhysicsBest wwCtrlErr avg{}_{\text{avg}}BaseErr ROI{}_{\text{ROI}} ( Δ\Delta = 0)Diversity
U-Net✗✗20.211±1.0970.211\pm 1.0973.267-
Fine LST✗✗30.746±0.3410.746\pm 0.3411.500.265±0.1830.265\pm 0.183
Coarse LST only✓✗80.882±0.3310.882\pm 0.3311.570.341±0.2400.341\pm 0.240
Coarse + Physics✓✓30.559±0.3100.559\pm 0.3101.6330.905±0.0520.905\pm 0.052
Table 2: Comparisons. We compare several configurations, each at the best ww and λ\lambda value (if applicable). As observed, our method (last row) produces the lowest CtrlErrCtrlErr and highest DiversityDiversity values.
Figure 6: Gain control. Controllability as a function of ww gain. Y-axis shows ROI Mean ΔT\Delta T Absolute Error (°C). Lower is better.
Figure 7: Realism Proxy. As a proxy for realism, we show radially averaged 2D Fourier power spectra of real and generated NDVI ROI patches. Power is averaged over frequency rings and plotted against normalized radial frequency (low: coarse structure; high: fine texture). Close alignment indicates similar spatial frequency statistics.
Figure 8: NDVI Diversity. We show tile-level NDVI variability observed in our dataset after binning tiles into similar building height and mean LST bins. Marker size corresponds to the standard deviation of NDVI within each bin (minimum count = 30). Standard deviations range from 0.09 to 0.16, indicating substantial within-bin variability.
Figure 9: Additional city-level qualitative results. Each row shows NDVI generation under Δ∈{−2,0,+2}∘\Delta\in\{-2,0,+2\}^{\circ} C with the ROI mean predicted change Δpred\Delta_{\text{pred}} .
Figure 9 (continued).
Figure 9 (continued).
Figure 9 (continued).
ParameterValue
Architecture
BackboneNCSN++
Image size128×128128\times 128
Base channels ( nfnf )128
Channel multipliers(1,2,2,2)(1,2,2,2)
Residual blocks / resolution4
Table 3: Inverse diffusion model hyperparameters.

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