MAGiDiff: Sampling the Photospheric Vector Field from UV/EUV Filtergrams

Ruoyu Wang; David Fouhey

astro-ph.SRSep 30, 2026

MAGiDiff: Sampling the Photospheric Vector Field from UV/EUV Filtergrams

Authors: Ruoyu Wang, David Fouhey

Organizations: NYU

Abstract

Photospheric vector magnetic fields are foundational to modeling, understanding, and forecasting solar activity. These data are usually produced by inverting and disambiguating the full Stokes vector at multiple passbands, which is demanding. Here, we investigate how well we can estimate photospheric vector magnetograms from UV/EUV filtergrams. This problem is challenging and intrinsically ambiguous without polarization information, as the mapping from UV/EUV intensity to the magnetic field is indirect and ill-posed. We introduce MAGiDiff, a machine-learning-based method that uses denoising diffusion models to estimate vector magnetograms from UV/EUV filtergrams. As input, MAGiDiff takes a stack of filtergrams from the Solar Dynamics Observatory (SDO) / Atmospheric Imaging Assembly (AIA); as output, it is trained to estimate the disambiguated vector magnetogram as seen by Hinode / Solar Optical Telescope-Spectro-Polarimeter (SOT-SP). We show that MAGiDiff can accurately mimic the Hinode ground-truth. Additionally, we probe MAGiDiff's understanding of the physical structure and magnetic connectivity. On full-disk, we show that it produces plausible structures for active regions. MAGiDiff generalizes across solar cycles despite hemispheric polarity reversal, and can be fine-tuned to other EUV instruments including STEREO/EUVI and GOES-R/SUVI. While clearly not a substitute for a dedicated instrument, MAGiDiff opens the door to new capabilities.

Figures & tables

Figure 1: Architecture of denoising U-Net used in MAGiDiff and illustration of the diffusion process. The denoising UNet takes noisy latent $\tilde{\mathbf{z}}_{t}$ at timestep $t$ together with conditioning input $\mathbf{c}$ as input and predicts the velocity $\hat{\mathbf{v}}_{t}$ — a linear combination of $\epsilon$ and $\mathbf{x}_{0}$ . In the forward process, the frozen VAE encoder maps an input magnetogram to a clean latent $\mathbf{z}$ , a timestep $t\in\{1,2,\cdots,T\}$ is sampled, and the scheduler corrupts $\mathbf{z}$ to $\tilde{\mathbf{z}}_{t}$ according to its noise schedule. The UNet is trained to regress the corresponding velocity target. At inference, sampling begins from $\tilde{\mathbf{z}}_{T}$ sampled from Gaussian noise, and iterates the reverse process: at each step the UNet takes noisy latent at current timestep $\tilde{\mathbf{z}}_{t}$ along with conditioning input $\mathbf{c}$ and predicts velocity $\hat{\mathbf{v}}_{t}$ . The scheduler then uses $\hat{\mathbf{v}}_{t}$ to remove noise from $\tilde{\mathbf{z}}_{t}$ . The final clean latent $\hat{\mathbf{z}}_{0}$ is decoded by the frozen VAE decoder to produce the predicted vector magnetogram. Both the forward and reverse diffusion processes operate entirely in latent space. The intermediate states shown in the figure therefore correspond to latent variables, which are decoded by the frozen VAE decoder and displayed in magnetogram space only for visual interpretability.

Figure 2: Architecture of Variational autoencoder and spatial rescaler used in MAGiDiff . The VAE consists of an encoder and a decoder: the encoder maps three-component vector magnetograms to a gaussian latent distribution parameterized by mean $\mu$ and log-variance $\log\boldsymbol{\sigma}^{2}$ , from which a latent code $z$ is sampled; the decoder reconstructs the magnetogram from $z$ . The spatial rescaler maps UV/EUV filtergrams—concatenated with auxiliary disk-mask and latitude channels—to a conditioning input $c$ at the latent’s spatial resolution, via three parallel branches: a multi-scale convolutional branch with cross-scale attention fusion, a learnable convolution branch, and a bilinear interpolation branch. These branch outputs are concatenated channel-wise and merged by a $1\times 1$ convolution.

Figure 3: A qualitative result of MAGiDiff on the test set with Hinode /SOT-SP as reference, with the corresponding pixel value distributions. Top row: selected input UV/EUV intensity images, left-to-right SDO /AIA 131Å, 171Å, 193Å, 304Å, 1600Å. Middle rows: Hinode /SOT-SP vector magnetogram and MAGiDiff prediction, left-to-right $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ . Bottom row: hexbin density plot of MAGiDiff predictions against Hinode /SOT-SP ground truth. In the hexbin panels, pixels with ground truth absolute value below $150$ Mx cm -2 are omitted to prevent low-amplitude quiet-Sun pixels dominating the pixel population. The gray dashed line marks the $1{:}1$ relation and the red line marks the least-squares fit. Each panel also reports the Pearson correlation coefficient (CC) and slope of the best fit line. MAGiDiff recovers the dominant magnetic structures and closely mimics Hinode /SOT-SP. In faint plage and quiet-Sun regions, MAGiDiff predictions are generally correct but can have reversed polarity and reduced detail. The hexbin panels confirm this agreement quantitatively, in which most pixel density concentrates near the $1{:}1$ relation. Example Date: 2016 April 11, 12:36 TAI. Colormaps: -3000 3000 Mx cm -2 using signed square root $x\mapsto\textrm{sign}(x)\sqrt{|x|}$ for contrast. Histogram legend: 1 1000 counts, shown logarithmically.

Figure 4: Pixel-value histograms and hexbin density plots of MAGiDiff predictions against Hinode /SOT-SP vector magnetograms on the test set. Each column corresponds to $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ , and $|\alpha\mathbf{B}|$ . The top panels compare the distributions of MAGiDiff predictions and the Hinode /SOT-SP ground truth. The bottom panel shows the corresponding hexbin density plot, together with a gray dashed line marking the $1{:}1$ relation, a red line marking the least-squares fit on all pixels, and a purple dashed line marking the least-squares fit on pixels for which the predicted sign agrees with the ground truth. Each panel lists the Pearson correlation coefficient (CC) and the coefficient of determination ( $R^{2}$ ), both computed over all plotted pixels, together with the slopes of the two fit lines. Density concentrated near the $1{:}1$ line indicates agreement between MAGiDiff prediction and ground truth. Deviations from this line are most apparent near the extremes of the ground-truth distribution, where MAGiDiff tends to underestimate field strengths. In $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ , a weaker concentration near the $y=-x$ relation indicates pixels for which MAGiDiff predicts approximately the correct magnitude but opposite sign. The faint horizontal concentration near $y=0$ marks pixels for which MAGiDiff predictions are close to zero despite having significant ground truth field strengths, usually due to misalignment or small magnetic fields without indications in UV/EUV. To make the trends more apparent, pixels with ground truth absolute value below $150$ Mx cm -2 are omitted from all panels, since low-amplitude quiet-Sun pixels dominate the full pixel population. Histogram legend: $100$ $100000$ count, shown logarithmically.

Model	Polarity Prior	Overall polarity $\uparrow$		Wrong-polarity rate by AR class $\downarrow$
		Pass ( $\tau\!<\!1$ )	Conf. ( $\tau\!<\!0.5$ )	QS/Plage	$\alpha$	$\beta$	$\beta\delta$	$\beta\gamma$	$\beta\gamma\delta$	All
Samples				1061	455	2490	112	1099	1077	6294
Distinct NOAA ARs				–	19	61	4	30	18	93
MAGiDiff $\pm\mathbf{B}$	$\times$	48.7	41.5	51.0	47.7	50.9	68.8	52.3	51.4	51.3
MAGiDiff No Polarity Prior	$\times$	86.7	76.6	15.3	20.0	12.7	8.9	10.0	13.9	13.3
MAGiDiff	✓	92.7	84.8	9.1	8.4	4.2	0.0	8.6	12.0	7.3

Table 1: The polarity prior improves MAGiDiff ’s overall polarity agreement. It is most effective where a clear leading–following polarity pair exists: bipolar

\beta

regions gain the most, while unipolar

\alpha

regions are frequently wrong with or without the prior and the most complex

\beta\gamma\delta

regions remain difficult. We evaluate MAGiDiff with and without the polarity prior on the test set, using one realization per input for each variant. The overall columns report the fraction of predictions with

\tau

below each threshold, where

\tau

is defined in Equation 5 :

\tau<1.0

indicates that the predicted polarity agrees with the ground truth better than its sign-flipped counterpart, while

\tau<0.5

gives a stricter measure of a confident polarity agreement. The remaining columns report the wrong-polarity rate (

\tau\geq 1

, lower is better) among valid test samples of each Mount Wilson active-region class, where each sample is labeled by the most complex NOAA active region within its valid ground-truth footprint and QS/Plage marks frames with no spotted region. The polarity prior column indicates whether latitude and solar cycle inputs are included during training.

Figure 5: Representative qualitative comparison of MAGiDiff , MAGiDiff without polarity prior, and MAGiDiff $\pm\mathbf{B}$ . From left to right, the figure shows the Hinode /SOT-SP $\alpha B_{R}$ reference, followed by $16$ realizations generated by MAGiDiff , MAGiDiff without polarity prior, and MAGiDiff $\pm\mathbf{B}$ , respectively. Realizations with incorrect polarity are outlined in red. Example date: 2016 September 5, 14:48 TAI. Colormaps: -3000 3000 Mx cm -2 following Figure 3 .

Panel of Figure 6 — Figure 6: Qualitative comparison of MAGiDiff and Regression U-Net baseline, with the corresponding gradient magnitude maps. Example date: 2016 June 15, 03:36 TAI. Both MAGiDiff and the regression baseline accurately predict the large-scale magnetic field structure. However, MAGiDiff additionally reproduces the realistic quiet-Sun texture as seen in Hinode /SOT-SP, whereas the regression baseline collapses the quiet Sun to an nonphysically smooth background. The gradient maps show that this smoothing is systematic, where the baseline underestimates the gradient magnitude in every component. Magnetogram colormap: -3000 3000 Mx cm -2 following Figure 3 . Gradient magnitude colormap: $0$ $250$ Mx cm -2 $\mathrm{pixel}^{-1}$ .

Measures	Metric	$\alpha B_{R}$			$\alpha B_{\phi}$			$\alpha B_{\theta}$			$\|\alpha\mathbf{B}\|$
Strong-field accuracy	MAE [Mx cm -2 ] $\downarrow$	612.5	$\|$	575.5	304.1	$\|$	304.3	296.4	$\|$	294.6	428.6	$\|$	372.8
Strong-field accuracy	% $<$ 300 $\uparrow$	46.3	$\|$	49.1	69.1	$\|$	69.8	70.6	$\|$	71.3	49.5	$\|$	57.0
Value-distribution match	$W_{1}$ [Mx cm -2 ] $\downarrow$	36.6	$\|$	14.9	30.7	$\|$	10.5	32.4	$\|$	10.9	64.8	$\|$	24.7
Global sharpness match	$\nabla$ -ratio $\rightarrow\!1$	0.39	$\|$	0.73	0.22	$\|$	0.62	0.21	$\|$	0.60	0.44	$\|$	0.71
Local sharpness accuracy	$\nabla$ -MAE [Mx cm -2 /px] $\downarrow$	41.84	$\|$	38.05	26.92	$\|$	20.93	27.35	$\|$	20.96	35.87	$\|$	34.72
Power-spectrum match	RALSD [dB] $\downarrow$	8.56	$\|$	4.25	11.32	$\|$	6.00	11.55	$\|$	5.96	7.98	$\|$	4.04

Table 2: MAGiDiff matches the regression baseline in per-pixel accuracy while substantially better reproducing the pixel-value distribution, sharpness, and power spectrum of the ground truth. We compare MAGiDiff with a regression U-Net baseline on the test set, using one prediction per input: a single sampled realization for MAGiDiff and the deterministic output of the baseline; each cell reports Baseline

|

MAGiDiff , with the better value in bold . For each field component, we report the mean absolute error (MAE, lower is better) and the percentage of pixels with error below

300

Mx cm -2 (%

<300

, higher is better), computed over strong-field pixels with

|\alpha\mathbf{B}|>1000

Mx cm -2 . The remaining metrics measure how well predictions reproduce the structure of the ground truth over all valid pixels:

W_{1}

reports the Wasserstein distance between the predicted and observed pixel-value distributions (lower is better); the

\nabla

-ratio compares the total gradient magnitude of the prediction to that of the ground truth, where values near 1 indicate matched sharpness and values below 1 indicate over-smoothing;

\nabla

-MAE reports the mean absolute error of the gradient magnitude (lower is better); and RALSD reports the radially averaged log-spectral distance between the predicted and observed power spectra (lower is better), computed on

256\times 256

crops for comparability. All metrics are computed after aligning the global polarity of each prediction with the Hinode /SOT-SP ground truth.

Figure 8: Pixel-wise correlation map on four test examples from 2016. Dates, top to bottom: Jan 26, 23:12 TAI; Apr 14, 02:48 TAI; Jul 19, 16:48 TAI; Oct 08, 09:12 TAI. For each panel: Top Row: Left to right: $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ , SDO /AIA $171$ Å, $1600$ Å. Bottom Row: Pixel-wise correlation of 5 selected pixels (labeled A-E ) with respect to all other pixels. As an example, we discuss results in the first panel with clear correlation clue. The sunspot pixel ( B ) accurately correlates with the sunspot region and its connected plage. The closed-loop footpoint ( C ) shows correlations that span the entire loop and show the correct opposite polarity at the conjugate footpoint. The quiet region ( E ) has near-zero correlations as expected. For reference, we also show ground truth Hinode /SOT-SP $\alpha B_{R}$ in Figure 16 . Colormaps: -3000 3000 Mx cm -2 for $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ following Figure 3 ; -1 1 for correlation maps. ( $1$ : correlated; $0$ : uncorrelated; $-1$ : anti-correlated).

Figure 9: Uncertainty map for four cutouts in Figure 8 . For each sample in Figure 8 , we present MAGiDiff ’s uncertainty estimates, defined as the per-pixel standard deviation divided by the per-pixel mean magnitude (a unitless measure). Example date: 2016 January 26, 23:12 TAI; 2016 April 14, 02:48 TAI; 2016 October 8, 09:12 TAI; 2016 July 19, 16:48 TAI. For each panel: Top Row: Left to right: $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ . Bottom Row: Left to right: Uncertainty map for $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ . Colormaps: -3000 3000 Mx cm -2 for $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ following Figure 3 ; 0 2 (unitless) for uncertainty maps.

Figure 10: Full-disk examples from 2016 February 5, 07:12 TAI. Upper Panel: Left to right: $\alpha B_{R}$ for SDO /HMI, SuperSynthIA, MAGiDiff . Bottom Panel: Left to right: $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ for region A and B. The magnetic field structure inferred by MAGiDiff largely mimics those of HMI and SuperSynthIA despite a preferential direction in some large-scale plage. We attribute this artifact to the patch-to-full disk domain gap: MAGiDiff is trained only on small, activity-focused patches and thus lacks global context. As a benefit of using higher-quality Hinode /SOT-SP magnetograms as label, MAGiDiff quiet region more closely resembles SuperSynthIA quiet region with reduced quiet-Sun noise artifacts. Colormaps: -3000 3000 Mx cm -2 following Figure 3 .

Figure 11: Full-disk $\alpha B_{R}$ predictions from MAGiDiff across multiple EUV instruments. Top row: Full-disk 171Å filtergrams from SDO /AIA, STEREO /EUVI, GOES–16 /SUVI, and GOES–18 /SUVI (left to right). Bottom row: SuperSynthIA $\alpha B_{R}$ reference followed by MAGiDiff $\alpha B_{R}$ predictions using full-disk STEREO /EUVI, GOES–16 /SUVI, and GOES–18 /SUVI filtergrams as input (left to right). MAGiDiff produces largely accurate full-disk magnetic field estimates across all three instruments, with active regions reproduced well. However, some predictions exhibit a preference for uniform polarity inconsistent with the SuperSynthIA reference, which we attribute to a domain gap arising from training exclusively on cropped regions. Colormaps: -3000 3000 Mx cm -2 following Figure 3 . Example Date: 2024 February 22, 04:12 TAI.

Figure 12: Zoomed-in view of cutouts from Figure 11 . Left to right: $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ for cutout region A and B . Top to bottom: MAGiDiff predictions from $3$ channel full-disk STEREO /EUVI EUV filtergrams, cropped post-inference to regions A and B (row 1), and inferred directly on the EUV cutouts of the same regions (row 2); same for $5$ channel GOES–16 /SUVI EUV filtergrams (rows 3 – 4) and $5$ channel GOES–18 /SUVI EUV filtergrams (rows 5 – 6); SuperSynthIA reference (row 7). Across all three instruments, MAGiDiff recovers the dominant magnetic field structures under both inference modes, and the predictions closely resemble the SuperSynthIA reference. Colormaps: -3000 3000 Mx cm -2 following Figure 3 . Example Date: 2024 February 22, 04:12 TAI.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Operation	Input	Output	Output Shape
Input Vector Magnetogram ( $\mathbf{B}$ )	-	-	$N\times 3\times H\times W$
VAE Encoding	$\mathbf{B}$	$\mu$ , $\log\boldsymbol{\sigma}^{2}$	$N\times 6\times h\times w$
Latent Sampling	$\mu$ , $\log\boldsymbol{\sigma}^{2}$	$\mathbf{z}$	$N\times 6\times h\times w$
VAE Decoding	$\mathbf{z}$	$\hat{\mathbf{B}}$	$N\times 3\times H\times W$
Loss Calculation	$\mathbf{B}$ , $\hat{\mathbf{B}}$ , $\mu$ , $\log\boldsymbol{\sigma}^{2}$	$\mathcal{L}$	-

Appendix

Table 3: Training Process of VAE

Operation	Input	Output	Output Shape
Input Vector Magnetogram ( $\mathbf{B}$ )	-	-	$N\times 3\times H\times W$
VAE Encoding	$\mathbf{B}$	$\mathbf{z}$	$N\times 6\times h\times w$
Forward Noising Process	$\mathbf{z}$ , $\epsilon$ , $t$	$\tilde{\mathbf{z}}_{t}$	$N\times 6\times h\times w$
Input Conditioning Information ( $\mathbf{I}$ )	-	-	$N\times 11\times H\times W$
Spatial Rescaler Encoding	$\mathbf{I}$	$\mathbf{c}_{\mathrm{sp}}$	$N\times 11\times h\times w$
Input Solar cycle Indicator ( $\mathbf{s}$ )	-	-	$N\times 1\times h\times w$

Appendix

Table 4: Training Process of Denoising Network

Operation	Input	Output	Output Shape
Input Noise ( $\tilde{\mathbf{z}}_{T}\sim\mathcal{N}(0,1)$ )	-	-	$N\times 6\times h\times w$
Input Conditioning Information ( $\mathbf{I}$ )	-	-	$N\times 11\times H\times W$
Spatial Rescaler Encoding	$\mathbf{I}$	$\mathbf{c}_{\mathrm{sp}}$	$N\times 11\times h\times w$
Input Solar cycle Indicator( $\mathbf{s}$ )	-	-	$N\times 1\times h\times w$
Concatenation of Conditioning Information	$\mathbf{c}_{\mathrm{sp}}$ , $\mathbf{s}$	$\mathbf{c}$	$N\times 12\times h\times w$
Repeat For Each Timestep $t\rightarrow t_{next}$ :	-	-	-

Appendix

Table 5: Inference Process of MAGiDiff

Figure 13: Additional qualitative results for MAGiDiff with Hinode /SOT-SP as reference. Example date: 2016 March 18, 23:36 TAI (upper panel); 2016 May 23, 01:12 TAI (lower panel). Colormaps: -3000 3000 Mx cm -2 following Figure 3 .

Figure 14: Additional qualitative results for MAGiDiff with Hinode /SOT-SP as reference. Example date: 2016 September 5, 14:24 TAI (upper panel); 2016 November 27, 19:36 TAI (lower panel). Colormaps: -3000 3000 Mx cm -2 following Figure 3 .

Figure 15: Representative examples of MAGiDiff predictions that contribute to $y=-x$ branch in Figure 4 . Example date: 2024 June 5, 08:12 TAI (upper panel); 2024 July 16, 20:00 TAI (lower panel). Colormaps: -3000 3000 Mx cm -2 following Figure 3 .

Figure 16: Ground Truth $\alpha B_{R}$ for four cutouts in Figure 8 . Example dates from left to right: 2016 January 26, 23:12 TAI; 2016 April 14, 02:48 TAI; 2016 July 19, 16:48 TAI; 2016 October 8, 09:12 TAI. Colormap: -3000 3000 Mx cm -2 following Figure 3 .

Figure 17: Consistency of MAGiDiff across multiple realizations for a single input. The leftmost column shows the full-field MAGiDiff prediction for $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ , with black boxes indicating the zoomed regions. The remaining columns show zoomed-in predictions from three independent realizations generated from the same input. The realizations show consistent magnetic structure and polarity across all three components, while retaining small-scale stochastic variations, an example of which is marked by red arrows. This example demonstrates that, for a fixed input, MAGiDiff defines a predictive distribution from which multiple plausible samples can be drawn. These samples remain largely consistent with one another in well-constrained regions, while allowing localized variation where signal is weak. Colormaps: -3000 3000 Mx cm -2 for $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ following Figure 3 . Data: 2016 January 26, 23:12 TAI.

Metric	$\alpha B_{R}$							$\alpha B_{\phi}$							$\alpha B_{\theta}$							$\|\alpha\mathbf{B}\|$
MAE [Mx cm -2 ] $\downarrow$	575.5	$\|$	552.1	$\|$	538.4	$\|$	533.1	304.3	$\|$	297.5	$\|$	293.3	$\|$	291.2	294.6	$\|$	286.3	$\|$	282.0	$\|$	280.0	372.8	$\|$	371.7	$\|$	370.9	$\|$	370.7
% $<$ 300 $\uparrow$	49.1	$\|$	49.9	$\|$	50.4	$\|$	50.6	69.8	$\|$	70.5	$\|$	71.0	$\|$	71.2	71.3	$\|$	72.1	$\|$	72.5	$\|$	72.7	57.0	$\|$	57.2	$\|$	57.3	$\|$	57.4
$W_{1}$ [Mx cm -2 ] $\downarrow$	14.9	$\|$	15.0	$\|$	15.0	$\|$	15.1	10.5	$\|$	10.5	$\|$	10.5	$\|$	10.5	10.9	$\|$	10.9	$\|$	10.9	$\|$	10.9	24.7	$\|$	24.8	$\|$	24.8	$\|$	24.9
$\nabla$ -ratio $\rightarrow\!1$	0.73	$\|$	0.73	$\|$	0.73	$\|$	0.73	0.62	$\|$	0.61	$\|$	0.61	$\|$	0.61	0.60	$\|$	0.60	$\|$	0.60	$\|$	0.60	0.71	$\|$	0.71	$\|$	0.71	$\|$	0.71
$\nabla$ -MAE [Mx cm -2 /px] $\downarrow$	38.05	$\|$	38.01	$\|$	38.00	$\|$	37.99	20.93	$\|$	20.92	$\|$	20.91	$\|$	20.91	20.96	$\|$	20.95	$\|$	20.94	$\|$	20.94	34.72	$\|$	34.68	$\|$	34.67	$\|$	34.66
RALSD [dB] $\downarrow$	4.25	$\|$	4.24	$\|$	4.24	$\|$	4.24	6.00	$\|$	6.00	$\|$	6.00	$\|$	6.00	5.96	$\|$	5.97	$\|$	5.97	$\|$	5.97	4.04	$\|$	4.04	$\|$	4.05	$\|$	4.04

Appendix

Table 6: Best-of-

N

selection improves MAGiDiff ’s per-pixel accuracy with diminishing returns, while a single realization already attains its full structural fidelity. We evaluate MAGiDiff on the test set when multiple attempts are permitted: for each input, MAGiDiff samples

N

candidate realizations, and we evaluate the candidate with the smallest error against the Hinode /SOT-SP ground truth. Each cell lists best-of-

N

for

N=1,4,16,32

, with the best value in bold . Metrics follow Table 2 : for each field component, MAE (lower is better) and %

<300

(higher is better) are computed over strong-field pixels with

|\alpha\mathbf{B}|>1000

Mx cm -2 , while

W_{1}

, the

\nabla

-ratio,

\nabla

-MAE, and RALSD measure how well predictions reproduce the pixel-value distribution, sharpness, and power spectrum of the ground truth over all valid pixels.

Figure 18: Hexbin density plots of MAGiDiff predictions against SuperSynthIA vector magnetograms for the full-disk sample shown in Figure 10 . From left to right, each column corresponds to $\alpha B_{R}$ , $\alpha B_{\phi}$ , $\alpha B_{\theta}$ , and $|\alpha\mathbf{B}|$ . From top to bottom, each row shows the hexbin plots for the full-disk, region A, and region B, respectively. Each panel shows the hexbin density together with a gray dashed line marking the $1{:}1$ relation and a red line marking the least-squares fit on all pixels. We also report the Pearson correlation coefficient (CC) and the slope of the fit line on top of each panel. Most of the density concentrates near the $1{:}1$ line, indicating strong agreement between MAGiDiff prediction and the reference SuperSynthIA magnetogram, with the strongest agreement observed in the most active region B. Pixels with ground truth absolute value below $150$ Mx cm -2 are omitted from all panels to make trends more apparent.

Metric	$\alpha B_{R}$							$\alpha B_{\phi}$							$\alpha B_{\theta}$							$\|\alpha\mathbf{B}\|$
MAE [Mx cm -2 ] $\downarrow$	779.0	$\|$	726.9	$\|$	692.1	$\|$	677.6	355.6	$\|$	335.3	$\|$	320.4	$\|$	315.6	354.7	$\|$	333.0	$\|$	317.1	$\|$	310.6	786.3	$\|$	739.9	$\|$	702.7	$\|$	687.4
% $<$ 300 $\uparrow$	19.9	$\|$	22.3	$\|$	24.2	$\|$	25.1	51.6	$\|$	54.1	$\|$	56.3	$\|$	56.9	52.0	$\|$	54.7	$\|$	56.9	$\|$	57.9	19.5	$\|$	22.0	$\|$	24.0	$\|$	25.0
$W_{1}$ [Mx cm -2 ] $\downarrow$	9.2	$\|$	9.3	$\|$	9.2	$\|$	9.2	4.6	$\|$	4.7	$\|$	4.6	$\|$	4.5	4.5	$\|$	4.5	$\|$	4.5	$\|$	4.4	12.7	$\|$	12.8	$\|$	12.7	$\|$	12.6
$\nabla$ -ratio $\rightarrow\!1$	0.75	$\|$	0.75	$\|$	0.75	$\|$	0.75	0.70	$\|$	0.70	$\|$	0.70	$\|$	0.70	0.70	$\|$	0.69	$\|$	0.69	$\|$	0.69	0.76	$\|$	0.75	$\|$	0.75	$\|$	0.75
$\nabla$ -MAE [Mx cm -2 /px] $\downarrow$	18.40	$\|$	18.28	$\|$	18.20	$\|$	18.16	5.27	$\|$	5.21	$\|$	5.17	$\|$	5.15	5.51	$\|$	5.45	$\|$	5.40	$\|$	5.39	18.03	$\|$	17.91	$\|$	17.83	$\|$	17.79
RALSD [dB] $\downarrow$	3.93	$\|$	3.93	$\|$	3.94	$\|$	3.96	4.73	$\|$	4.71	$\|$	4.70	$\|$	4.70	4.16	$\|$	4.14	$\|$	4.14	$\|$	4.15	3.85	$\|$	3.85	$\|$	3.86	$\|$	3.88

Appendix

Table 7: On the more challenging STEREO /EUVI cutouts, the fine-tuned MAGiDiff still produces reasonable estimates, and best-of-

k

sampling improves performance. Evaluation setup follows Table 6 .

Metric	$\alpha B_{R}$							$\alpha B_{\phi}$							$\alpha B_{\theta}$							$\|\alpha\mathbf{B}\|$
MAE [Mx cm -2 ] $\downarrow$	805.0	$\|$	747.6	$\|$	709.4	$\|$	695.9	348.4	$\|$	326.0	$\|$	311.3	$\|$	306.2	354.3	$\|$	331.4	$\|$	315.8	$\|$	309.9	791.7	$\|$	750.9	$\|$	717.3	$\|$	704.2
% $<$ 300 $\uparrow$	19.2	$\|$	21.5	$\|$	23.4	$\|$	24.1	53.0	$\|$	55.7	$\|$	57.7	$\|$	58.5	52.3	$\|$	54.9	$\|$	57.1	$\|$	57.9	19.3	$\|$	21.4	$\|$	23.3	$\|$	24.1
$W_{1}$ [Mx cm -2 ] $\downarrow$	8.1	$\|$	8.1	$\|$	8.1	$\|$	8.0	4.2	$\|$	4.3	$\|$	4.2	$\|$	4.2	4.1	$\|$	4.1	$\|$	4.1	$\|$	4.0	11.4	$\|$	11.5	$\|$	11.4	$\|$	11.3
$\nabla$ -ratio $\rightarrow\!1$	0.78	$\|$	0.78	$\|$	0.78	$\|$	0.78	0.72	$\|$	0.71	$\|$	0.71	$\|$	0.71	0.72	$\|$	0.72	$\|$	0.71	$\|$	0.72	0.79	$\|$	0.78	$\|$	0.78	$\|$	0.78
$\nabla$ -MAE [Mx cm -2 /px] $\downarrow$	19.12	$\|$	18.99	$\|$	18.90	$\|$	18.86	5.37	$\|$	5.32	$\|$	5.27	$\|$	5.26	5.62	$\|$	5.56	$\|$	5.51	$\|$	5.50	18.73	$\|$	18.61	$\|$	18.51	$\|$	18.48
RALSD [dB] $\downarrow$	2.72	$\|$	2.73	$\|$	2.72	$\|$	2.72	3.70	$\|$	3.73	$\|$	3.72	$\|$	3.72	3.65	$\|$	3.65	$\|$	3.65	$\|$	3.64	2.69	$\|$	2.70	$\|$	2.70	$\|$	2.69

Appendix

Table 8: On strong-field GOES /SUVI cutouts, the fine-tuned MAGiDiff produces reasonable estimates, with best-of-

k

sampling improves performance. Evaluation setup follow Table 6 .

Figure 19: Pixel-value histograms comparing MAGiDiff predictions with the corresponding SuperSynthIA vector magnetograms for the full-disk observation shown in Figure 11 . From left to right, each column correspond to

\alpha B_{R}

\alpha B_{\phi}

\alpha B_{\theta}

, and

|\alpha\mathbf{B}|

. From top to bottom, the row correspond to full-disk STEREO /EUVI, GOES–16 /SUVI, and GOES–18 /SUVI predictions, respectively.

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