Image Fidelity is Not Field Fidelity: Joint Thermodynamic Reconstruction and Error Localization in Neural Tomography

Alan Hsu; Jenna Samra; Alin Razvan Paraschiv; Liam Connor

cs.LGSep 24, 2026

Image Fidelity is Not Field Fidelity: Joint Thermodynamic Reconstruction and Error Localization in Neural Tomography

Authors: Alan Hsu, Jenna Samra, Alin Razvan Paraschiv, Liam Connor

Organizations: Harvard University Cambridge, MA, USA · Center for Astrophysics | Harvard & Smithsonian Cambridge, MA, USA · National Solar Observatory Boulder, CO, USA

Abstract

Neural fields for scientific tomography are optimized from 2D images, but the actual quantity of interest is often a latent 3D physical field. Because the forward map is many-to-one, low 2D image error need not certify a correct 3D field. Moreover, the latent field is not directly supervised during training, and its error cannot be evaluated against truth at deployment. We develop CoroNeRF to jointly optimize 3D electron density and temperature fields directly from multiview, multiline intensities through a differentiable atomic-emission renderer. Using solar coronal tomography as a controlled testbed, we evaluate physical-field recovery and test whether cross-seed instability provides a ground-truth-free-at-inference indicator of local physical-field error. We underscore the following two observations. (i) Image fidelity is not field fidelity: spectral ablations show that limited-channel reconstructions can fit their available observations well while recovering substantially worse fields, whereas evaluation on a common richer probe exposes the discrepancy. (ii) Cross-seed instability ranks local physical-field error across tested matched-model conditions, supported by sparsification and physical signal-strength controls. Seed-deviation projections provide complementary directional validation, but shared forward-model mismatch can still produce incorrect cross-seed consensus. These results characterize joint thermodynamic recovery and the usefulness and limits of seed-based error localization in a controlled, single-scene solar tomography testbed.

Figures & tables

Figure 1: CoroNeRF overview. The left $2\times 2$ grid displays multiline coronal observations of four spectral channels (Fe XIII $1075/1080$ nm, Si IX $2585/3935$ nm) forward-rendered from a PSI cube. The observations are used to fit a multiresolution hash-grid neural plasma field through the same differentiable renderer by minimizing an image loss (right panel). The fitted neural field yields jointly recovered 3D density and temperature fields.

Figure 2: Density-field reconstruction (given GT temperature) at $1.51$ R ⊙ . Each panel is a shell unraveled on a latitude-longitude plot. The top row shows the ground truth and reconstructions using a classical grid with Tikhonov regularization, positional encoder + MLP, and hash grid + decoder MLP representations. The bottom row shows corresponding residuals $\Delta\log_{10}n_{e}=\log_{10}n_{e,\mathrm{pred}}-\log_{10}n_{e,\mathrm{GT}}$ . The hash grid is able to reproduce sharper small-scale features, substantially reducing inner-band $\operatorname{MAE}$ relative to the MLP by more than $2\times$ and classical grid methods by about $4\times$ .

Figure 3: LOS projections of the jointly-reconstructed column density (top) and total-emissivity-weighted temperature (bottom), using a multiresolution hash-grid representation trained on all four spectral channels (Appendix A.3 ).

Figure 4: Image fidelity is not field fidelity. We show 3D density field-space $\operatorname{MAE}$ vs 2D held-out image-space loss. Each marker is a trained model (color $=$ number of spectral lines, shape $=$ the specific line set). The left plot uses held-out image error measured on each model’s own channels, which is a GT-free image-space validation quantity available on held-out observed views. Single-channel models achieve lower observed-channel image error than the four-line model despite having substantially larger field error. Evaluation on a common four-line probe (right panel) exposes these failures and largely restores the density-error ranking, showing that the low observed-channel image error of these configurations reflects limited spectral coverage rather than correct field recovery.

Figure 5: Noise-view sweep, fixed at 4 matched-model spectral channels, of $n_{\rm e}$ and $T_{\rm e}$ $\operatorname{MAE}$ . With at least $100$ views, field recovery remains accurate across the tested noise levels under the noise-matched loss. Severe angular undersampling substantially increases error and makes the reconstruction much more vulnerable to noise.

Figure 6: Ensemble panels of the 3D density field at $1.51$ R ⊙ using the canonical high-noise condition. We show the ensemble mean $\overline{m}(\mathbf{x})$ , ensemble-mean error $\epsilon_{\rm mean}(\mathbf{x})$ , and cross-seed instability $\sigma_{\rm ens}(\mathbf{x})$ . The maps exhibit similar spatial structure, which we quantify using correlations below.

Figure 7: Left panel plots Spearman rank correlation between the true ensemble mean error $\epsilon_{\rm mean}$ and $\sigma_{\rm ens}$ (green circle), inverse-emissivity $b_{\mathcal{E}}$ (orange), and partial correlation $\rho(\sigma_{\rm ens},\epsilon_{\rm mean}\,|\,b_{\mathcal{E}})$ (green triangle), showing that the rank association persists after controlling for the oracle inverse-emissivity proxy. Error bars are $95\%$ within-scene longitude-slice bootstrap intervals. We find that $\sigma_{\rm ens}$ localizes error in three matched-model regimes: noiseless, sparse-view, and high-noise, outperforming the emissivity proxy $b_{\mathcal{E}}$ . The partial correlation shows that the rank association remains after conditioning on an oracle inverse-emissivity proxy. Finally, we note that the localization of $\sigma_{\rm ens}$ deteriorates substantially under positive Si over-scaling and approaches chance for density at $a=1.4$ , but under-scaling retains partial localization ability; while $b_{\mathcal{E}}$ can still track the high-error, low-emissivity regions in this regime, it requires the GT field and is thus used only as an oracle baseline. The right panel consists of sparsification curves for the canonical noisy condition, showing that $\sigma_{\rm ens}$ tracks the oracle more closely than does the baseline $b_{\mathcal{E}}$ (nAUSE of $0.27$ compared to $0.52$ ).

Figure 8: Per-field error-energy capture computed by projecting the error onto ensemble deviation subspaces. Rank-9 seed-deviation spans capture $2.4$ - $32.1\%$ of the signed field error energy (green), which is above the $0.2\%$ isotropic reference (dashed red). Split-seed evaluation, using span and error from disjoint seed halves (orange), shows that the directional overlap persists when the span and target error are constructed from disjoint seed subsets. We additionally find that the original unrotated capture exceeds the longitude-rotation-null mean (purple) in all tested matched-model regimes and lies at the top of the tested rotation distribution in 11 of 12 combinations. Finally, we note that capture is largest under sparse-view and high-noise regimes.

Appendix figures & tables30 assets

Supplementary material from the paper’s appendix.

Appendix

step size	$\Delta s$ (R ⊙ )	rel-L2 vs finest	$\operatorname{asinhErr}$ vs finest
$1/128$	$0.234$	$20.6\%$	$1.0\times 10^{-2}$
$\mathbf{1/256}$ (production)	$0.117$	$7.5\%$	$1.7\times 10^{-3}$
$1/512$	$0.059$	$2.3\%$	$5.7\times 10^{-4}$
$1/1024$	$0.029$	— (ref)	— (ref)

Appendix

Table 1: Convergence table for selected renderer step sizes. For each step size, we render eight views using the GT cube and compute relative L2 and

\operatorname{asinhErr}

compared to the finest resolution.

Figure 9: Ensemble reconstruction panels of the 3D density (top) and temperature (bottom) fields at $1.51$ R ⊙ in the high-noise regime ( $\eta=9,V=300,\text{all four lines},a=1$ ). We show the ensemble mean $\overline{m}(\mathbf{x})$ (Equation 18 ), ensemble-mean error $\epsilon_{\rm mean}(\mathbf{x})$ (unobservable, Equation 20 ), and cross-seed instability $\sigma_{\rm ens}(\mathbf{x})$ (Equation 19 ).

Condition	$\rho(\sigma_{\rm ens},\epsilon_{\rm mean})$ $\uparrow$	$\rho(b_{\mathcal{E}},\epsilon_{\rm mean})$	partial $\rho(\sigma_{\rm ens},\epsilon_{\rm mean}\,\|\,b_{\mathcal{E}})$ $\uparrow$	$\rho(\sigma_{\rm ens},b_{\mathcal{E}})$
noiseless ( $300$ v)	$0.761_{-0.029}^{+0.022}$	$0.072_{-0.058}^{+0.052}$	$0.759_{-0.027}^{+0.022}$	$0.081$
$100$ views	$0.773_{-0.027}^{+0.021}$	$0.085_{-0.056}^{+0.050}$	$0.772_{-0.025}^{+0.020}$	$0.086$
$20$ views	$0.778_{-0.034}^{+0.029}$	$-0.019_{-0.056}^{+0.045}$	$0.780_{-0.035}^{+0.029}$	$0.038$
$5$ views	$0.712_{-0.050}^{+0.042}$	$-0.103_{-0.094}^{+0.088}$	$0.708_{-0.051}^{+0.043}$	$-0.161$
Noise $\times 9$	$0.572_{-0.052}^{+0.041}$	$0.405_{-0.042}^{+0.038}$	$0.447_{-0.059}^{+0.052}$	$0.621$
Noise $\times 25$	$0.555_{-0.055}^{+0.039}$	$0.438_{-0.044}^{+0.036}$	$0.393_{-0.059}^{+0.052}$	$0.663$

Appendix

Table 2: (Density) Pairwise Spearman correlations between cross-seed instability

\sigma_{\rm ens}

, ensemble mean error

\epsilon_{\rm mean}

, and emissivity proxy

b_{\mathcal{E}}

Condition	$\rho(\sigma_{\rm ens},\epsilon_{\rm mean})$ $\uparrow$	$\rho(b_{\mathcal{E}},\epsilon_{\rm mean})$	partial $\rho(\sigma_{\rm ens},\epsilon_{\rm mean}\,\|\,b_{\mathcal{E}})$ $\uparrow$	$\rho(\sigma_{\rm ens},b_{\mathcal{E}})$
noiseless ( $300$ v)	$0.726_{-0.027}^{+0.025}$	$0.001_{-0.066}^{+0.067}$	$0.732_{-0.027}^{+0.024}$	$0.122$
$100$ views	$0.732_{-0.023}^{+0.019}$	$0.014_{-0.068}^{+0.063}$	$0.735_{-0.022}^{+0.019}$	$0.115$
$20$ views	$0.717_{-0.034}^{+0.031}$	$0.092_{-0.055}^{+0.053}$	$0.716_{-0.032}^{+0.029}$	$0.061$
$5$ views	$0.611_{-0.041}^{+0.034}$	$0.015_{-0.057}^{+0.049}$	$0.626_{-0.040}^{+0.032}$	$-0.189$
Noise $\times 9$	$0.590_{-0.046}^{+0.044}$	$0.325_{-0.052}^{+0.046}$	$0.521_{-0.049}^{+0.046}$	$0.579$
Noise $\times 25$	$0.601_{-0.049}^{+0.042}$	$0.382_{-0.051}^{+0.045}$	$0.503_{-0.058}^{+0.047}$	$0.624$

Appendix

Table 3: (Temperature) Pairwise Spearman correlations between cross-seed instability

\sigma_{\rm ens}

, ensemble mean error

\epsilon_{\rm mean}

, and emissivity proxy

b_{\mathcal{E}}

Condition	pooled	$r=1.33$ R ⊙	$r=1.61$ R ⊙	$r=1.89$ R ⊙
noiseless ( $300$ v)	$0.76$ [ $0.76$ ]	$0.74$ [ $0.74$ ]	$0.77$ [ $0.75$ ]	$0.76$ [ $0.75$ ]
$100$ views	$0.77$ [ $0.77$ ]	$0.75$ [ $0.75$ ]	$0.78$ [ $0.77$ ]	$0.77$ [ $0.75$ ]
$20$ views	$0.78$ [ $0.78$ ]	$0.78$ [ $0.78$ ]	$0.78$ [ $0.78$ ]	$0.76$ [ $0.73$ ]
$5$ views	$0.71$ [ $0.71$ ]	$0.68$ [ $0.68$ ]	$0.75$ [ $0.75$ ]	$0.61$ [ $0.60$ ]
Noise $\times 9$	$0.57$ [ $0.45$ ]	$0.59$ [ $0.58$ ]	$0.54$ [ $0.44$ ]	$0.41$ [ $0.20$ ]
Noise $\times 25$	$0.56$ [ $0.39$ ]	$0.53$ [ $0.51$ ]	$0.54$ [ $0.41$ ]	$0.38$ [ $0.15$ ]

Appendix

Table 4: (Density) Per-shell correlation

\rho(\sigma_{\rm ens},\epsilon_{\rm mean})

(partial

\rho(\sigma_{\rm ens},\epsilon_{\rm mean}\,|\,b_{\mathcal{E}})

in brackets), for selected conditions.

Condition	pooled	$r=1.33$ R ⊙	$r=1.61$ R ⊙	$r=1.89$ R ⊙
noiseless ( $300$ v)	$0.73$ [ $0.73$ ]	$0.70$ [ $0.70$ ]	$0.72$ [ $0.70$ ]	$0.77$ [ $0.75$ ]
$100$ views	$0.73$ [ $0.74$ ]	$0.73$ [ $0.73$ ]	$0.70$ [ $0.68$ ]	$0.76$ [ $0.75$ ]
$20$ views	$0.72$ [ $0.72$ ]	$0.72$ [ $0.73$ ]	$0.67$ [ $0.65$ ]	$0.75$ [ $0.72$ ]
$5$ views	$0.61$ [ $0.63$ ]	$0.70$ [ $0.72$ ]	$0.50$ [ $0.50$ ]	$0.53$ [ $0.51$ ]
Noise $\times 9$	$0.59$ [ $0.52$ ]	$0.66$ [ $0.66$ ]	$0.54$ [ $0.45$ ]	$0.49$ [ $0.30$ ]
Noise $\times 25$	$0.60$ [ $0.50$ ]	$0.61$ [ $0.61$ ]	$0.55$ [ $0.44$ ]	$0.50$ [ $0.29$ ]

Appendix

Table 5: (Temperature) Per-shell correlation

\rho(\sigma_{\rm ens},\epsilon_{\rm mean})

(partial

\rho(\sigma_{\rm ens},\epsilon_{\rm mean}\,|\,b_{\mathcal{E}})

in brackets), for selected conditions.

Figure 10: Density-error sparsification curves for the noiseless, high-noise, sparse-view, and Si-mismatch regimes. Lower remaining MAE is better, and the random reference is the exact expected uniform-retention curve.

Condition	$\operatorname{AUSE}_{\sigma}$	$\operatorname{AUSE}_{b}$	$\operatorname{nAUSE}_{\sigma}$	$\operatorname{nAUSE}_{b}$
noiseless ( $300$ v)	$0.0021$	$0.0145$	$0.115_{-0.012}^{+0.019}$	$0.809_{-0.096}^{+0.120}$
$100$ views	$0.0021$	$0.0147$	$0.113_{-0.012}^{+0.016}$	$0.794_{-0.094}^{+0.115}$
$20$ views	$0.0062$	$0.0657$	$0.117_{-0.020}^{+0.026}$	$1.239_{-0.102}^{+0.101}$
$5$ views	$0.0327$	$0.1834$	$0.222_{-0.035}^{+0.043}$	$1.245_{-0.135}^{+0.139}$
Noise $\times 9$	$0.0085$	$0.0161$	$0.274_{-0.036}^{+0.047}$	$0.520_{-0.063}^{+0.075}$
Noise $\times 25$	$0.0108$	$0.0168$	$0.304_{-0.044}^{+0.056}$	$0.472_{-0.055}^{+0.067}$

Appendix

Table 6: (Density) Sparsification summary for selected ranking metrics across selected conditions.

Condition	$\operatorname{AUSE}_{\sigma}$	$\operatorname{AUSE}_{b}$	$\operatorname{nAUSE}_{\sigma}$	$\operatorname{nAUSE}_{b}$
noiseless ( $300$ v)	$0.0008$	$0.0052$	$0.140_{-0.025}^{+0.028}$	$0.855_{-0.156}^{+0.190}$
$100$ views	$0.0009$	$0.0051$	$0.142_{-0.026}^{+0.029}$	$0.838_{-0.152}^{+0.184}$
$20$ views	$0.0017$	$0.0098$	$0.161_{-0.026}^{+0.033}$	$0.910_{-0.123}^{+0.144}$
$5$ views	$0.0065$	$0.0240$	$0.281_{-0.031}^{+0.037}$	$1.037_{-0.085}^{+0.092}$
Noise $\times 9$	$0.0025$	$0.0060$	$0.251_{-0.045}^{+0.052}$	$0.599_{-0.107}^{+0.130}$
Noise $\times 25$	$0.0030$	$0.0061$	$0.266_{-0.042}^{+0.056}$	$0.550_{-0.095}^{+0.121}$

Appendix

Table 7: (Temperature) Sparsification summary for selected ranking metrics across selected conditions.

Condition	$n_{\rm e}$ full $\rho$	$n_{\rm e}$ LOO $\rho$	$n_{\rm e}$ LOO $\operatorname{nAUSE}_{\sigma}$	$T_{\rm e}$ full $\rho$	$T_{\rm e}$ LOO $\rho$	$T_{\rm e}$ LOO $\operatorname{nAUSE}_{\sigma}$
$300$ views	$0.761$	$[0.755,0.767]$	$[0.115,0.120]$	$0.726$	$[0.717,0.735]$	$[0.138,0.144]$
$100$ views	$0.773$	$[0.765,0.775]$	$[0.112,0.128]$	$0.732$	$[0.726,0.735]$	$[0.141,0.145]$
$20$ views	$0.778$	$[0.773,0.783]$	$[0.114,0.124]$	$0.717$	$[0.708,0.722]$	$[0.160,0.166]$
$5$ views	$0.712$	$[0.695,0.731]$	$[0.205,0.240]$	$0.611$	$[0.599,0.619]$	$[0.276,0.293]$
Noise $\times 9$	$0.572$	$[0.559,0.568]$	$[0.280,0.287]$	$0.590$	$[0.582,0.590]$	$[0.251,0.262]$
Noise $\times 25$	$0.555$	$[0.540,0.552]$	$[0.307,0.324]$	$0.601$	$[0.585,0.603]$	$[0.263,0.286]$

Appendix

Table 8: Leave-one-out (LOO) ranges of

\rho(\sigma_{\rm ens},\epsilon_{\rm mean})

and

\operatorname{nAUSE}_{\sigma}

for both density and temperature.

Condition	$E_{\rm cap}$ $\%$	$E_{\rm cap}/E_{\rm cap}^{\rm rand}$ (enrichment)	$E_{\rm cap}^{B\rightarrow A}$ $\%$	rot-null $\mu$ $\%$	$E_{\rm cap}$ rot $\%$
noiseless ( $300$ v)	$7.5$	$36\times$	$3.6^{+2.7}_{-3.3}$	$2.5$	$100$
$100$ views	$4.8$	$23\times$	$2.5^{+2.7}_{-2.2}$	$2.1$	$100$
$20$ views	$27.2$	$130\times$	$14.4^{+8.6}_{-8.0}$	$5.5$	$100$
$5$ views	$32.1$	$154\times$	$17.9^{+11.6}_{-13.3}$	$20.9$	$100$
Noise $\times 9$	$6.0$	$29\times$	$2.7^{+2.3}_{-2.0}$	$0.9$	$100$
Noise $\times 25$	$11.0$	$53\times$	$5.9^{+4.7}_{-4.4}$	$2.3$	$100$

Appendix

Table 9: (Density) Error-capture diagnostics as an additional field-space consistency metric.

Condition	$E_{\rm cap}$ $\%$	$E_{\rm cap}/E_{\rm cap}^{\rm rand}$ (enrichment)	$E_{\rm cap}^{B\rightarrow A}$ $\%$	rot-null $\mu$ $\%$	$E_{\rm cap}$ rot $\%$
noiseless ( $300$ v)	$5.0$	$24\times$	$2.6^{+2.0}_{-1.9}$	$1.5$	$100$
$100$ views	$2.4$	$11\times$	$1.2^{+1.4}_{-0.9}$	$1.4$	$79$
$20$ views	$20.5$	$98\times$	$11.0^{+7.7}_{-7.3}$	$4.0$	$100$
$5$ views	$24.0$	$115\times$	$12.8^{+8.3}_{-8.3}$	$18.7$	$100$
Noise $\times 9$	$9.3$	$45\times$	$4.6^{+3.1}_{-3.6}$	$2.1$	$100$
Noise $\times 25$	$20.6$	$99\times$	$12.8^{+7.0}_{-7.0}$	$3.4$	$100$

Appendix

Table 10: (Temperature) Error-capture diagnostics as an additional field-space consistency metric.

Group	Name	Description
Rendering	AABB	$x_{\rm AABB}\in[-1,1]^{3}$
	sample step size	$dx_{\rm AABB}=1/256$
	LOS integration	midpoint Riemann sum
Architecture	hash grid	$2^{20}$ hash map, $\times 2$ features
	levels	$20$ levels, $16\rightarrow 512$ coarse-to-fine resolutions
	MLP head	per-field, $2$ hidden layers, width $64$

Appendix

Table 11: Table of canonical hyperparameters used in CoroNeRF. Note that the listed

s_{c}

values are the base scales used for

\eta\leq 1

. For

\eta>1

s_{c}

is multiplied by

\sqrt{\eta}

as described in Appendix D.6 . The ordering of

\alpha_{c}

and

s_{c}

values corresponds to Fe XIII 1075, Fe XIII 1080, Si IX 2585, and Si IX 3935, respectively.

Figure 11: Density-field reconstruction (with GT temperature supplied) at $0^{\circ}$ longitude, spanning $[1.1,3.0]$ R ⊙ . Each panel is a meridional slice (latitude-radius plot). The top row shows the ground truth and reconstructions using classical spherical grid with Tikhonov regularization, positional-encoder + MLP, and hash grid + decoder head representations. The bottom row shows corresponding signed residuals $\Delta\log_{10}n_{e}=\log_{10}n_{e,\mathrm{pred}}-\log_{10}n_{e,\mathrm{GT}}$ . The multiresolution hash grid is able to reconstruct consistent radial structures much farther out than the classical method, and achieves lower errors on the inner radial boundaries near the photosphere.

Model	$\text{MAE}_{\text{inner}}(\log_{10}n_{\rm e})$ $\downarrow$	$\text{AbsRel}_{\text{inner}}(n_{\rm e})$ $\downarrow$	$\text{asinhErr}(I)$ $\downarrow$	$\text{PSNR}(I)$ $\uparrow$
Hash20	$\mathbf{0.042\pm<0.001}$	$\mathbf{0.094\pm<0.001}$	$\mathbf{0.003\pm<0.001}$	$\mathbf{39.59\pm 0.67}$
Hash17	$\mathbf{0.042\pm<0.001}$	$0.095\pm<0.001$	$0.004\pm 0.001$	$38.77\pm 0.65$
MLP	$0.097\pm 0.001$	$0.254\pm 0.004$	$0.024\pm 0.003$	$24.65\pm 0.62$
Grid-Reg	$0.168\pm<0.001$	$0.449\pm<0.001$	$0.053\pm<0.001$	$11.57\pm<0.01$
Grid	$0.217\pm<0.001$	$0.571\pm<0.001$	$0.080\pm<0.001$	$11.30\pm<0.01$

Appendix

Table 12: Density representation benchmark. Each row indicates a model configuration, and metrics are reported as mean

\pm

standard deviation over 3 seeds, with deviations below

5\times 10^{-4}

reported as

<0.001

. The first column indicates the experiment family, and the last four columns are the relevant metrics. Image metrics are averaged over views and channels, and density metrics are averaged over inner coronal radial shells

1.1

2

R ⊙ . The multiresolution hash grid outperforms the MLP by more than

2\times

, and the classical grid by about

4\times

Figure 12: Density and temperature reconstructed residuals for different loss metric settings. We find that the Gaussian-only loss performs worst while the asinh-only loss performs best, with hybrid losses landing in between the two regimes.

Objective	$\text{MAE}_{\text{inner}}(\log_{10}n_{\rm e})$ $\downarrow$	$\text{MAE}_{\text{inner}}(\log_{10}T_{\rm e})$ $\downarrow$	$\text{asinhErr}(I)$ $\downarrow$
Gaussian-only $\lambda_{G}=1$	$0.145\pm 0.010$	$0.075\pm 0.020$	$0.060\pm 0.006$
Fixed hybrid $\lambda_{G}=10^{-1}$	$0.134\pm 0.009$	$0.064\pm 0.014$	$0.047\pm 0.005$
Fixed hybrid $\lambda_{G}=10^{-3}$	$0.087\pm 0.001$	$0.036\pm 0.001$	$0.032\pm 0.002$
Fixed hybrid $\lambda_{G}=10^{-5}$	$0.061\pm 0.002$	$0.022\pm 0.002$	$\mathbf{0.021\pm<0.001}$
Fixed asinh only $\lambda_{G}=0$	$\mathbf{0.047\pm 0.001}$	$0.017\pm<0.001$	$0.022\pm<0.001$
Target- $\sigma$ asinh $\lambda_{G}=0$	$0.047\pm<0.001$	$\mathbf{0.016\pm<0.001}$	$0.022\pm 0.001$

Appendix

Table 13: Loss ablation benchmark. For the Gaussian-only experiment,

\lambda_{A}=0

, otherwise it is fixed at

\lambda_{A}=1

. We find that objectives that favor the asinh term

\mathcal{L}_{A}

generally perform better than those that favor the heteroscedastic Gaussian loss term.

Exp	$b$	$s$	$V$	$D$	MAE ( $\log_{10}n_{e}$ ) $\downarrow$	PSNR (I) $\uparrow$	MSE ( $\log_{10}I$ ) $\downarrow$
big	$4096$	$60$ k	$30$	$64$	$0.096$	$30.56$	$1.75\times 10^{-4}$
big	$4096$	$60$ k	$1000$	$256$	$0.097$	$30.74$	$1.78\times 10^{-4}$
med	$4096$	$30$ k	$1000$	$256$	$0.106$	$26.60$	$5.46\times 10^{-4}$
med	$4096$	$30$ k	$30$	$64$	$0.107$	$27.47$	$4.81\times 10^{-4}$
base	$1024$	$30$ k	$1000$	$256$	$0.109$	$24.88$	$6.40\times 10^{-4}$
base	$1024$	$30$ k	$30$	$64$	$0.109$	$27.82$	$5.01\times 10^{-4}$

Appendix

Table 14: Compute-quality trade-off ablation study. We vary the batch size

b

, steps

s

, views

V

, and image dimension

D

. We find that the log-density

\operatorname{MAE}

varies modestly across the tested settings, with slightly better performance at

b=4096

s=60

Channel Set	$\text{MAE}_{\text{inner}}(\log_{10}n_{\rm e})$ $\downarrow$	$\text{MAE}_{\text{inner}}(\log_{10}T_{\rm e})$ $\downarrow$	asinhErr (observed channels) $\downarrow$
all4	$\mathbf{0.039\pm<0.001}$	$\mathbf{0.014\pm<0.001}$	$0.008\pm 0.002$
Fe XIII pair	$0.097\pm 0.004$	$0.023\pm 0.001$	$0.009\pm 0.003$
Si IX pair	$0.068\pm 0.001$	$0.058\pm 0.001$	$\mathbf{0.004\pm 0.001}$
Fe $1075$	$0.605\pm 0.004$	$0.072\pm<0.001$	$0.006\pm 0.001$
Si $3935$	$0.530\pm 0.028$	$0.195\pm 0.006$	$0.005\pm 0.002$

Appendix

Table 15: Reconstruction metrics for our spectral ablation study. The four-line configuration achieves the lowest field errors and low across-seed variability in this three-seed ablation. We can also observe that a good image-space reconstruction does not imply a good physical-field reconstruction: while the Si IX pair has the lowest image-space validation loss, it still has higher physical-field errors.

Figure 13: Field Reconstruction at three selected radii: $1.20,1.51,1.90$ R ⊙ (columns). We show the field-space GT, prediction, and signed residuals $\Delta m=\hat{m}-m^{*}$ for $m\in\{\log_{10}n_{\rm e},\log_{10}T_{\rm e}\}$ .

Figure 14: Field-space $\operatorname{MAE}$ radial dependence for the spectral ablation study. Color denotes the number of spectral lines, and marker shape denotes the line set. We find that having at least a pair of lines substantially reduces radial errors across $1.1$ - $3$ R ⊙ .

Figure 15: 3D field-space $\operatorname{MAE}$ vs 2D held-out image-space validation loss, showing that a good image-space reconstruction need not imply a good field-space reconstruction. Each point is one seed from the spectral ablation benchmark trained with different sets of spectral channels. We find that fewer-channel models can achieve lower observed-channel image error than the four-line model despite worse field recovery.

Figure 16: Robustness in physical field reconstruction. The columns show ground truth and the reconstructed density (top row) and temperature (bottom row) for different combinations of views and noise multipliers. We see that with 300 views, there is moderate degradation between a clean reconstruction with no noise and one with a noise multiplier of 25, while retaining low absolute error. However, once we reduce the number of views significantly to 20 views (last column), the combined effect of a large noise multiplier and sparse views is a failure mode for physical field reconstruction.

Noise Setting	$\text{MAE}_{\text{inner}}(\log_{10}n_{\rm e})$ $\downarrow$	$\text{MAE}_{\text{inner}}(\log_{10}T_{\rm e})$ $\downarrow$	$\text{asinhErr}(I)$ $\downarrow$
$\eta=0$ , 5 views	$0.410\pm 0.020$	$0.070\pm 0.005$	$1.454\pm 0.041$
$\eta=0$ , 20 views	$0.122\pm 0.023$	$0.026\pm 0.003$	$0.458\pm 0.060$
$\eta=0$ , 100 views	$0.039\pm{<}0.001$	$0.014\pm{<}0.001$	$0.007\pm 0.001$
$\eta=0$ , 300 views	$0.039\pm{<}0.001$	$0.014\pm{<}0.001$	$0.007\pm 0.001$
$\eta=1$ , 5 views	$0.516\pm 0.026$	$0.126\pm 0.010$	$1.513\pm 0.046$
$\eta=1$ , 20 views	$0.209\pm 0.018$	$0.044\pm 0.003$	$0.823\pm 0.050$

Appendix

Table 16: Noise-view stress benchmark results (also shown in Figure 5 in the main text). With sufficient angular coverage, the reconstruction remains robust even under strong heteroscedastic observation noise: increasing the noise multiplier to

\times 25

at 300 training views only moderately increases the density and temperature field errors. In contrast, sparse-view regimes are substantially less stable, and the combination of high noise and sparse views produces a clear failure mode in latent physical-field recovery. The training objective uses the noise-matched

s_{c}

scaling described above, while held-out asinhErr is evaluated on noise-free held-out views using the same base per-channel scales across all

\eta

Figure 17: Demonstration of the accompanying denoising effect in the framework. We show the clean ground truth target, and sample noisy training observations. The final column shows a reconstructed render using a model trained on noise $\times 25$ images, where multiview consistency suppresses pixel-scale noise in the reconstructed render.

Figure 18: Errors in physical field reconstruction due to forward model mismatch. The columns show ground truth and the reconstructed density (top row) and temperature (bottom row) for different abundance mismatch scales. We see a clear failure mode when the Si IX intensities are scaled by $\pm 40\%$ : the reconstructed field has spurious sharp features that do not exist in the ground truth fields.

$a$	$\text{asinhErr}(I)$ $\downarrow$	$n_{\rm e}$ $\operatorname{MAE}$ $\downarrow$	$n_{\rm e}$ $\operatorname{ME}$	$T_{\rm e}$ $\operatorname{MAE}$ $\downarrow$	$T_{\rm e}$ $\operatorname{ME}$
$0.6$	$0.030\pm<0.001$	$0.301\pm 0.006$	$-0.211\pm 0.004$	$0.076\pm 0.001$	$-0.030\pm 0.002$
$0.8$	$0.017\pm<0.001$	$0.146\pm 0.005$	$-0.076\pm 0.004$	$0.036\pm 0.001$	$-0.010\pm 0.001$
$1.0$	$\mathbf{0.006\pm<0.001}$	$\mathbf{0.039\pm<0.001}$	$-0.001\pm 0.001$	$\mathbf{0.014\pm<0.001}$	$\mathbf{0.000\pm<0.001}$
$1.2$	$0.016\pm<0.001$	$0.092\pm 0.001$	$0.062\pm 0.001$	$0.023\pm<0.001$	$-0.002\pm<0.001$
$1.4$	$0.027\pm<0.001$	$0.142\pm 0.001$	$0.107\pm 0.001$	$0.031\pm<0.001$	$-0.006\pm<0.001$

Appendix

Table 17: Abundance-mismatch benchmark. We scale the Si IX intensity channels in the synthetic observations by

a

while evaluating against the clean ground-truth physical fields.

\operatorname{MAE}

reports inner-band absolute log-field error, while ME reports signed inner-band errors. The clean setting, corresponding to scale

1.0

, gives the lowest image and field errors. Scaling the Si IX channels below or above the correct value produces systematic signed density errors, indicating that forward-model mismatch can be absorbed into incorrect latent physical fields.

Figure 19: LOS projections of recovered column density for selected conditions and view angles.

Figure 20: LOS projections of recovered emissivity-weighted temperature for selected conditions and view angles.

Figure 21: LOS projections of total-emissivity log-intensities for selected conditions and view angles.

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