GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors

Wangqian Chen; Hao Wang; Yumeng Zhang; Jiajia Guo; Junting Chen; Jun Zhang

cs.LGSep 28, 2026

GPARA: Graph-Posterior-Aligned Refinement and Active Acquisition for Grounding Diffusion Priors

Authors: Wangqian Chen, Hao Wang, Yumeng Zhang, Jiajia Guo, Junting Chen, Jun Zhang

Organizations: The Hong Kong University of Science and Technology · The Chinese University of Hong Kong, Shenzhen

Abstract

Active grounding of a frozen diffusion prior requires jointly determining where new measurements should be taken and how they should be used to refine the current reconstruction. Posterior-ensemble-based methods can estimate acquisition utility from generated samples, but require repeated ensemble generation as observations accumulate and capture posterior geometry only through empirical statistics. This paper proposes GPARA, which learns a context-dependent graph surrogate over diffusion prediction residuals, inducing an explicitly reusable posterior response operator that propagates measurement innovations to unobserved variables and evaluates candidate measurements through weighted posterior-risk reduction. Under the matched surrogate, we show that the same response operator also determines expected one-step acquisition benefit and yields an analytic ranking consistent with expected reconstruction improvement. A bounded learned residual calibrates the analytic utility to account for surrogate mismatch, while a small prior ensemble is generated once and reconditioned to update risk weights without repeated diffusion posterior sampling during acquisition. Experiments on two reconstruction tasks spanning physical field and computer vision show consistent improvements in refinement and active acquisition over the evaluated baselines. Ablations further support the complementary roles of step-wise graph refinement, adaptive risk weighting, and analytically anchored calibration.

Figures & tables

Figure 1: Active grounding of a frozen diffusion prior. A task-specific conditional prior is pretrained offline and frozen. At deployment, context alone may produce an instance-mismatched prediction, and sparse target measurements are thus acquired to ground the prior to the current realization.

Figure 2: Overview of GPARA. Stage I performs response-aligned active acquisition: the graph posterior specifies how information propagates, while a state-adaptive risk matrix specifies where uncertainty reduction is valuable. A bounded residual scorer calibrates the analytic utility. After reaching the sensing budget, Stage II fixes the acquired observations and reuses the same graph-posterior conditioner to refine prediction throughout the reverse diffusion process.

Figure 3: Posterior refinement across observation rates. RMSE as a function of the fraction of observed target locations for (a) RFR and (b) DC. All methods use the same frozen DDPM prior and identical randomly sampled observations at every observation rate.

Method	Radio-field reconstruction				Depth completion
	RMSE $\downarrow$	MAE $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$
DDPM	0.035 $\pm$ 0.003	0.025	0.926	30.2	0.350 $\pm$ 0.005	0.273	0.113	0.878
DPS	0.031 $\pm$ 0.002	0.021	0.937	31.1	0.347 $\pm$ 0.005	0.271	0.112	0.881
DDNM	0.033 $\pm$ 0.003	0.023	0.919	30.6	0.344 $\pm$ 0.005	0.267	0.110	0.883
FPS	0.034 $\pm$ 0.003	0.024	0.921	30.4	0.345 $\pm$ 0.004	0.269	0.111	0.883
DiffPIR	0.030 $\pm$ 0.002	0.021	0.934	31.2	0.342 $\pm$ 0.004	0.266	0.110	0.885

Table 1: Posterior refinement under 491 matched random observations, approximately

3\%

of RFR and

1\%

of DC target entries. RMSE is reported as mean

\pm

standard deviation across five independent seeds; other metrics show the mean values.

Figure 4: Qualitative comparison of active acquisition and reconstruction. The first two rows show RFR examples with $10\%$ observations, and the last two rows are DC examples under $5\%$ .

Method	Radio-field reconstruction				Depth completion
	RMSE $\downarrow$	MAE $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$	RMSE $\downarrow$	MAE $\downarrow$	AbsRel $\downarrow$	$\delta_{1}$ $\uparrow$
ADS	0.026 $\pm$ 0.001	0.018	0.947	33.1	0.338 $\pm$ 0.002	0.267	0.111	0.882
AdaSense + DPS	0.026 $\pm$ 0.001	0.018	0.947	33.2	0.339 $\pm$ 0.002	0.268	0.111	0.881
AdaSense + DDNM	0.028 $\pm$ 0.002	0.020	0.937	32.7	0.336 $\pm$ 0.002	0.267	0.110	0.883
AdaSense + FPS	0.029 $\pm$ 0.002	0.021	0.935	32.5	0.336 $\pm$ 0.002	0.266	0.110	0.883
AdaSense + DiffPIR	0.026 $\pm$ 0.001	0.018	0.948	33.4	0.334 $\pm$ 0.002	0.264	0.110	0.885

Table 2: Active acquisition with a matched 491-point sensing budget across five independent seeds.

Model	Injection	RFR	DC
Point Bayes	Step-wise	0.0327	0.346
Uniform graph	Final-only	0.0240	0.309
Learn Graph	Final-only	0.0233	0.307
Uniform graph	Step-wise	0.0195	0.267
Learn Graph	Step-wise	0.0191	0.262

Table 4: Mechanism ablations of GPARA . (a) Compares posterior mechanisms under identical random observations. (b) Compares acquisition criteria while keeping others fixed.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Method	5 steps	10 steps	20 steps	50 steps	100 steps	500 steps
DDPM	0.035 $\pm$ 0.0034	0.030 $\pm$ 0.0006	0.030 $\pm$ 0.0014	0.030 $\pm$ 0.0010	0.030 $\pm$ 0.0009	0.031 $\pm$ 0.0009
DPS	0.031 $\pm$ 0.0023	0.028 $\pm$ 0.0006	0.028 $\pm$ 0.0013	0.027 $\pm$ 0.0009	0.024 $\pm$ 0.0003	0.018 $\pm$ 0.0002
DDNM	0.033 $\pm$ 0.0031	0.028 $\pm$ 0.0005	0.028 $\pm$ 0.0013	0.027 $\pm$ 0.0009	0.027 $\pm$ 0.0007	0.027 $\pm$ 0.0009
FPS	0.034 $\pm$ 0.0033	0.027 $\pm$ 0.0005	0.027 $\pm$ 0.0009	0.026 $\pm$ 0.0002	0.025 $\pm$ 0.0003	0.022 $\pm$ 0.0004
DiffPIR	0.030 $\pm$ 0.0021	0.027 $\pm$ 0.0006	0.026 $\pm$ 0.0008	0.026 $\pm$ 0.0003	0.025 $\pm$ 0.0003	0.021 $\pm$ 0.0004
GPARA	0.019 $\pm$ 0.0007	0.017 $\pm$ 0.0002	0.016 $\pm$ 0.0003	0.016 $\pm$ 0.0002	0.016 $\pm$ 0.0001	0.016 $\pm$ 0.0002

Appendix

Table 5: Sensitivity to the number of reverse diffusion steps on RFR under

3\%

random observations. Results are full-region RMSE (mean

\pm

standard deviation) over five paired seeds.

Score	RFR		DC
Score	Spearman $\uparrow$	Regret ( $\times 10^{-5}$ ) $\downarrow$	Spearman $\uparrow$	Regret ( $\times 10^{-4}$ ) $\downarrow$
High-accuracy analytic	0.42 $\pm$ 0.26	1.26 $\pm$ 1.45	0.19 $\pm$ 0.27	9.23 $\pm$ 15.60
Deployed analytic	0.35 $\pm$ 0.27	1.14 $\pm$ 1.35	0.11 $\pm$ 0.25	9.51 $\pm$ 15.52
Calibrated utility	0.40 $\pm$ 0.25	1.06 $\pm$ 1.25	0.15 $\pm$ 0.24	3.60 $\pm$ 4.97
Direct learned scorer	0.44 $\pm$ 0.29	0.94 $\pm$ 1.28	0.23 $\pm$ 0.27	6.08 $\pm$ 14.75

Appendix

Table 6: Alignment between acquisition scores and empirical one-step reconstruction benefit under shared random prefixes.

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