GeoCFM: Positive-Only Conditional Flow Matching for Mineral Occurrence Sampling

Moshe Eliasof; Eldad Haber

cs.LGSep 28, 2026

GeoCFM: Positive-Only Conditional Flow Matching for Mineral Occurrence Sampling

Authors: Moshe Eliasof, Eldad Haber

Organizations: Faculty of Computer and Information Science, Ben-Gurion University of the Negev, Israel · Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Canada

Abstract

Critical mineral discovery is a positive-only problem: deposits are observed as sparse locations, while unlabeled regions are not reliable negatives, and similar geophysical signatures can arise from different subsurface states. We therefore model mineral targeting as learning a conditional spatial distribution over occurrence locations, $π(p\mid d)$ , given geo-images $d$ , rather than predicting a deterministic per-pixel score map. We introduce GeoCFM, a conditional flow-matching model that generates mineral occurrence point sets conditioned on multi-channel geo-images; GeoCFM learns a point-wise transport field in $\mathbb{R}^2$ , using UNet features with point-conditioned velocity prediction to bridge dense rasters and sparse supervision without pseudo-negatives. On a synthetic magnetics--geochemistry benchmark with latent activation and on USGS Earth MRI data with a spatially disjoint tile split, GeoCFM improves geometric agreement with observed occurrences over score-map and non-conditional baselines, while representing epistemic uncertainty through conditional sampling.

Figures & tables

Panel of Figure 1 — Figure 1 : Mineral prospectivity as a Positive-Only learning problem. Left: Standard supervised learning relies on both known positives and confirmed negatives to learn a decision boundary. Middle: The reality of mineral exploration is positive-only; we observe sparse positive deposits, but the remaining area is unknown/unlabeled (absence of a mine is not evidence of absence). Right: Our GeoCFM approach models a conditional density over mineral occurrences given geo-images, directly yielding a probabilistic mineral discovery map from positive samples alone.

Figure 2 : Magnetics (left), gravity (middle), and topography (right) together with mineral (gold or copper) occurrences, i.e., deposits, in a geo-image over North America.

Figure 3 : Synthetic magnetics–geochemistry benchmark. From left to right: (1) observed RTP magnetic geo-image $d$ ; (2) contact-zone proxy $\|\nabla d\|$ with sampled deposit locations overlaid (cyan); (3) hidden geochemistry $s$ (background) with contours of the observed proxy $t$ , illustrating that $t$ only partially reflects the latent control; (4) observed geochemistry proxy $t$ ; (5) the same deposit set overlaid on $d$ (green, 500 points). Multiple magnetic rings are present, but deposits activate only a subset and localize along arcs, reflecting unobserved geochemical controls and motivating conditional density modeling of occurrence locations.

Figure 4 : GeoCFM point-conditioned velocity prediction. The geo-image $d$ is encoded by a UNet into a dense feature map. For the current set of noised points $p_{t}$ (with $N$ points), we bilinearly sample local features to obtain an $N\times D$ feature matrix, concatenate each feature with the point coordinate (and time embedding), and pass the result through a shared per-point network to predict velocities $v_{\theta}(p_{t},t\mid d)\in\mathbb{R}^{N\times 2}$ , which define the point transport in the flow ODE.

Panel of Figure 5 — Figure 5 : Uncertainty and prospectivity maps. Top: synthetic input and true deposits, the oracle density, and the conditional densities recovered by GeoCFM, OCSVM, and Retrieval-KDE. Bottom: Earth MRI input and true occurrences with the same three methods. GeoCFM concentrates density on the relevant occurrence structures, exposing epistemic uncertainty through the spread of its conditional density, whereas the one-class and retrieval baselines produce diffuse or misplaced densities.

Panel of Figure 6 — Figure 6 : Synthetic benchmark: true occurrences and four GeoCFM samples conditioned on the same input. Samples align with magnetic contact zones and activate only a subset of anomalies, demonstrating one-to-many conditional behavior.

Method	CD $\downarrow$	Sink. $\downarrow$	F@5 $\uparrow$	NLL $\downarrow$	Top5 $\uparrow$
UNet-Seg	$29.46\pm 2.18$	$0.100\pm 0.006$	$0.615\pm 0.022$	$9.143\pm 0.089$	$0.661\pm 0.031$
GBDT	$32.13\pm 2.03$	$0.103\pm 0.006$	$0.546\pm 0.018$	$9.288\pm 0.083$	$0.630\pm 0.027$
RF	$37.09\pm 2.17$	$0.116\pm 0.006$	$0.462\pm 0.018$	$9.552\pm 0.054$	$0.586\pm 0.025$
Poisson-LR	$39.93\pm 2.16$	$0.122\pm 0.006$	$0.384\pm 0.016$	$9.803\pm 0.042$	$0.500\pm 0.028$
OCSVM	$45.56\pm 2.20$	$0.134\pm 0.007$	$0.246\pm 0.015$	$10.557\pm 0.020$	$0.236\pm 0.018$
Retrieval-KDE	$47.16\pm 2.86$	$0.132\pm 0.007$	$0.220\pm 0.016$	$13.302\pm 0.440$	$0.058\pm 0.011$

Table 1 : Synthetic benchmark results, averaged over

20

stochastic draws across

50

held-out examples; values are mean

\pm

standard deviation of the mean. We report Chamfer distance (CD, pixels), Sinkhorn OT divergence (Sink.), F@5, KDE negative log-likelihood (NLL), and top-5% hit rate (Top5). Arrows indicate the better direction; the best value in every column is in bold. Baselines are grouped by family (pseudo-negative score-map models; one-class and retrieval-conditioned estimators; non-conditional samplers), and GeoCFM is shown in the last row.

Figure 7 : Earth MRI: Qualitative comparison of conditional mineral occurrence draws. (Left) True mineral occurrence locations (black triangles) overlaid on a held-out geophysics geo-image tile, showing a central cluster. (Draws 1–4) Four unique sampled occurrence locations (green dots) generated by our GeoCFM, all overlaid on the same true occurrences and background geophysics geo-image, demonstrating its ability to capture the complex, non-isotropic distribution of mineral potential and expose non-identifiability. We provide additional examples and comparisons with baselines in the supplementary material.

Method	CD $\downarrow$	Sink. $\downarrow$	F@5 $\uparrow$	NLL $\downarrow$	Top5 $\uparrow$
UNet-Seg	$46.81\pm 2.30$	$0.205\pm 0.008$	$0.085\pm 0.006$	$11.620\pm 0.290$	$0.130\pm 0.013$
GBDT	$52.98\pm 2.14$	$0.215\pm 0.007$	$0.069\pm 0.004$	$11.233\pm 0.269$	$0.102\pm 0.010$
RF	$54.37\pm 2.23$	$0.225\pm 0.008$	$0.071\pm 0.004$	$11.504\pm 0.297$	$0.095\pm 0.011$
Poisson-LR	$64.21\pm 2.26$	$0.255\pm 0.008$	$0.055\pm 0.004$	$11.274\pm 0.239$	$0.059\pm 0.008$
OCSVM	$58.38\pm 2.33$	$0.240\pm 0.008$	$0.053\pm 0.003$	$11.946\pm 0.313$	$0.059\pm 0.008$
Retrieval-KDE	$61.14\pm 2.34$	$0.250\pm 0.008$	$0.053\pm 0.003$	$11.698\pm 0.298$	$0.061\pm 0.009$

Table 2 : Earth MRI results with a spatially disjoint (tile-based) train/test split, on the test split, averaged over

20

stochastic draws across

200

patches; values are mean

\pm

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Synthetic	Earth MRI
Input channels	2 ( $d,t$ )	8 geophysical layers
Base UNet width $nf$	32	48
UNet depth	3	3
Feature dimension $D$	64	128
Time-embedding dimension	64	64
Velocity head	residual network	MLP

Appendix

Table 3 : GeoCFM architecture settings used in the two benchmarks.

Setting	Synthetic	Earth MRI
Batch size	4	8
Learning rate	$3\times 10^{-4}$	$3\times 10^{-4}$
Weight decay	$10^{-4}$	$10^{-4}$
Maximum iterations	500,000	400,000
Gradient clip	1.0	1.0
Validation interval	250 iterations	2,000 iterations

Appendix

Table 4 : GeoCFM optimization settings used in the two benchmarks.

Panel of Figure 8 — Figure 8 : Additional qualitative comparisons on held-out Earth MRI patches. Each row shows one held-out patch. From left to right, the columns correspond to ground truth, GeoCFM, Random Uniform, KDE, Random Forest, UNet Segmentation, and Poisson Logistic. Black triangles denote observed mineral occurrences, and green points denote sampled occurrences. GeoCFM produces samples that are more spatially concentrated around the observed structures than the unconditional or score-map baselines, while still expressing uncertainty through repeated draws.

	Synthetic		Earth MRI
Method	Train CD $\downarrow$	Test CD $\downarrow$	Train CD $\downarrow$	Test CD $\downarrow$
Uniform sampling	49.30	49.61	63.99	64.25
Global KDE	37.12	41.16	57.10	66.35
Poisson-LR	38.75	39.93	62.80	64.21
Random Forest	32.08	37.09	49.12	54.37
UNet-Seg	26.11	29.46	41.30	46.81

Appendix

Table 5 : Train vs. test Chamfer distance (pixels, lower is better) on both benchmarks. The Earth MRI split is spatially disjoint (tile-based).

Data	Pos. frac.	CD $\downarrow$	Sink. $\downarrow$	NLL $\downarrow$	F@5 $\uparrow$
Synthetic	$100\%$	$9.38\pm 0.09$	$0.0447\pm 0.0006$	$8.96\pm 0.07$	$0.633\pm 0.005$
Synthetic	$75\%$	$9.62\pm 0.10$	$0.0457\pm 0.0006$	$8.87\pm 0.06$	$0.636\pm 0.005$
Synthetic	$50\%$	$9.60\pm 0.14$	$0.0460\pm 0.0010$	$9.01\pm 0.06$	$0.627\pm 0.005$
Earth MRI	$100\%$	$12.35\pm 0.21$	$0.085\pm 0.002$	$10.76\pm 0.15$	$0.151\pm 0.006$
Earth MRI	$75\%$	$11.91\pm 0.17$	$0.076\pm 0.002$	$10.63\pm 0.16$	$0.189\pm 0.007$
Earth MRI	$50\%$	$12.46\pm 0.19$	$0.084\pm 0.002$	$10.39\pm 0.11$	$0.159\pm 0.007$

Appendix

Table 6 : Positive-subset stability. GeoCFM is retrained with different fractions of the available positives over three seeds; we report mean

\pm

std across seeds.

Data	Method	ms/patch $\downarrow$	CD $\downarrow$	F@5 $\uparrow$
Synthetic	UNet-Seg	13.92	29.46	0.615
Synthetic	GeoCFM $K=5$	19.79	9.30	0.580
Synthetic	GeoCFM $K=10$	21.98	9.39	0.610
Synthetic	GeoCFM $K=50$	38.47	9.37	0.634
Earth MRI	UNet-Seg	12.50	46.81	0.085
Earth MRI	GeoCFM $K=5$	16.95	12.00	0.140

Appendix

Table 7 : Inference cost vs. number of Euler steps

K

, compared with the single-pass UNet-Seg baseline. Runtime is milliseconds per patch.

Budget $N$	100	250	500	1000	2000
Synthetic NLL $\downarrow$	11.79	10.96	10.79	10.66	10.56
Synthetic stab. $\uparrow$	0.894	0.946	0.970	0.982	0.988
Earth MRI NLL $\downarrow$	10.20	9.32	9.24	9.02	8.99
Earth MRI stab. $\uparrow$	0.876	0.962	0.971	0.984	0.991

Appendix

Table 8 : Effect of the Monte Carlo sampling budget

N

on density quality (KDE-NLL, lower is better) and density stability (higher is better).

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