N-Tree Diffusion for Long-Horizon Wildfire Risk Forecasting

Yucheng Xing; Xin Wang

cs.LGMar 7, 2026

N-Tree Diffusion for Long-Horizon Wildfire Risk Forecasting

Authors: Yucheng Xing, Xin Wang

Organizations: Department of Electrical and Computer Engineering, Stony Brook University, Stony Brook, NY 11794, USA

Abstract

Long-horizon wildfire risk forecasting requires generating probabilistic spatial fields under sparse event supervision while maintaining computational efficiency across multiple prediction horizons. Extending diffusion models to multi-step forecasting typically repeats the denoising process independently for each horizon, leading to redundant computation. We introduce N-Tree Diffusion (NT-Diffusion), a hierarchical diffusion model designed for long-horizon wildfire risk forecasting. Fire occurrences are represented as continuous Fire Risk Maps (FRMs), which provide a smoothed spatial risk field suitable for probabilistic modeling. Instead of running separate diffusion trajectories for each predicted timestamp, NT-Diffusion shares early denoising stages and branches at later levels, allowing horizon-specific refinement while reducing redundant sampling. We evaluate the proposed framework on a newly collected real-world wildfire dataset constructed for long-horizon probabilistic prediction. Results indicate that NT-Diffusion achieves consistent accuracy improvements and reduced inference cost compared to baseline forecasting approaches.

Figures & tables

Panel of Figure 1 — Figure 1: Illustration of the Fire Risk Map (FRM).(a) shows a single fire occurrence in the area and (b) presents its Gaussian risk representation. For multiple real fire events occurring in the region corresponding to the real map, as depicted in (c), the resulting FRM is generated as shown in (d).

Figure 2: Two extreme computational structures for multi-horizon diffusion generation. (a) Fully shared reverse trajectory. (b) Fully independent reverse trajectories.

Figure 3: Illustration of NT-Diffusion with

L=4

hierarchical layers, where reverse trajectories are partially shared and progressively branched across horizons.

Figure 4: Illustration of the diffusion denoising process at noise level

s

and time

t

	Quality ( $\times$ 1e-2, $\downarrow$ )			Efficiency ( $\downarrow$ )
	RMSE	MAE	KL	Time	FLOPs	Params
LSTM [ 28 ]	6.15 $\pm$ 0.13	2.10 $\pm$ 0.01	5.58 $\pm$ 0.25	2.12 $\pm$ 0.17	36.24	1342.32
ULSTM [ 4 ]	6.85 $\pm$ 1.89	1.84 $\pm$ 0.96	6.32 $\pm$ 2.33	2.54 $\pm$ 0.02	5.30	26.51
CNN [ 54 ]	6.23 $\pm$ 0.49	2.25 $\pm$ 0.93	5.68 $\pm$ 0.45	47.16 $\pm$ 0.04	174.16	3.49
ConvLSTM [ 29 ]	11.49 $\pm$ 1.47	4.76 $\pm$ 1.60	19.73 $\pm$ 12.19	7.75 $\pm$ 0.10	9.77	1.02
Transformer [ 7 ]	6.35 $\pm$ 0.01	2.30 $\pm$ 0.08	6.64 $\pm$ 0.24	8.13 $\pm$ 0.09	466.68	253.97

Table 1: Overall performance comparison among different fire forecasting models.

	Quality ( $\times$ 1e-2, $\downarrow$ )			Efficiency ( $\downarrow$ )
	RMSE	MAE	KL	Time	FLOPs	Params
Diffusion(2D-AR)	5.87 $\pm$ 0.01	1.13 $\pm$ 0.00	5.17 $\pm$ 0.01	727.62 $\pm$ 2.95	32.42	5.89
Diffusion(2D-Attn)	5.94 $\pm$ 0.03	1.16 $\pm$ 0.01	5.27 $\pm$ 0.04	32.18 $\pm$ 0.24	34.60	14.29
Diffusion(3D)	5.94 $\pm$ 0.02	1.15 $\pm$ 0.01	5.27 $\pm$ 0.03	99.05 $\pm$ 0.39	83.67	12.60
Diffusion(ViT)	5.95 $\pm$ 0.04	1.25 $\pm$ 0.02	5.30 $\pm$ 0.06	94.75 $\pm$ 0.29	63.64	38.88
NT-Diffusion	5.86 $\pm$ 0.04	1.16 $\pm$ 0.01	5.16 $\pm$ 0.05	30.35 $\pm$ 0.22	18.36	6.23

Table 2: Comparison among different diffusion-based models (steps=10, mean

\pm

std, Bold : best, Underline : second best).

Figure 5: Comparison of execution time (ms) among diffusion-based models with different steps.

Figure 6: Comparison of average FLOPs of our model with different hyperparameter

L

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

$D_{test}$	NT-Diffusion				NT-Diffusion
$D_{test}$	2D-AR	2D-Attn	3D	ViT	NT-Diffusion
10	727.62 $\pm$ 2.95	32.18 $\pm$ 0.24	99.05 $\pm$ 0.39	94.75 $\pm$ 0.29	30.35 $\pm$ 0.22
20	1469.10 $\pm$ 5.65	63.32 $\pm$ 0.37	195.13 $\pm$ 0.14	190.27 $\pm$ 1.24	59.58 $\pm$ 0.55
50	3631.94 $\pm$ 56.94	156.24 $\pm$ 0.88	492.57 $\pm$ 0.47	465.52 $\pm$ 1.16	147.63 $\pm$ 0.28
100	7239.19 $\pm$ 45.91	310.76 $\pm$ 0.80	990.10 $\pm$ 12.14	929.37 $\pm$ 6.20	292.92 $\pm$ 1.50
200	14282.82 $\pm$ 69.74	628.90 $\pm$ 1.82	1993.92 $\pm$ 8.39	1848.71 $\pm$ 1.48	583.50 $\pm$ 0.59

Appendix

Table 3: Comparison of average execution time (ms, mean

\pm

std) among diffusion-based models with different diffusion steps

D_{test}

( Bold : best).

$D_{test}$	NT-Diffusion
$D_{test}$	$L=1$	$L=2$	$L=4$	$L=8$
10	30.95 $\pm$ 1.08	30.44 $\pm$ 0.29	30.35 $\pm$ 0.22	30.94 $\pm$ 0.36
20	60.70 $\pm$ 0.30	60.21 $\pm$ 0.42	59.58 $\pm$ 0.55	60.66 $\pm$ 0.33
50	151.18 $\pm$ 1.95	149.64 $\pm$ 2.40	147.63 $\pm$ 0.28	149.41 $\pm$ 2.73
100	296.95 $\pm$ 5.00	295.43 $\pm$ 0.38	292.92 $\pm$ 1.50	296.16 $\pm$ 2.73
200	592.16 $\pm$ 2.00	586.79 $\pm$ 1.61	583.50 $\pm$ 0.59	591.32 $\pm$ 4.10

Appendix

Table 4: Comparison of average execution time (ms, mean

\pm

std) of our model with different hyperparameter

L

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