Foundation models for astronomical surveys offer powerful learned representations that can be transferred to downstream regression tasks such as galaxy property estimation. However, point predictions alone are insufficient for scientific inference; reliable uncertainty quantification (UQ) is essential. We compare seven UQ methods on galaxy property regression using frozen AION-1 foundation-model embeddings, predicting redshift, stellar mass, stellar-population age, gas-phase metallicity, and specific star-formation rate, from Legacy Survey photometry/imaging and DESI spectra, with PROVABGS-derived labels. Distribution-free conformal methods achieve marginal coverage within $\sim$1\,pp of the nominal 90\% across all properties, while non-conformal baselines (Deep Ensembles, MC~Dropout) fail to calibrate reliably. Among conformal approaches, Conformalized Quantile Regression (CQR) delivers the best coverage in the bin with the poorest model predictions. More importantly, only the Locally Valid and Discriminative (LVD) framework -- particularly when operating on AION-1 embeddings -- also provides finite-sample \emph{local validity}, producing intervals that adapt to each galaxy's local prediction difficulty rather than relying on marginal guarantees alone. These results establish conformal prediction, and LVD in particular, as the preferred UQ framework for uncertainty-aware inference on foundation-model embeddings in astrophysics.
Routine full-disk EUV imaging has been available only since the modern era, such as SOHO and SDO. To extend EUV coronal context into earlier periods, we leverage the multi-decade availability of full-disk \HeI{} observations, whose absorption is modulated by coronal irradiance and magnetic topology and is widely used as a proxy for open-field regions. We present a diffusion-based conditional image translation framework, Coronal Hole-aware Diffusion Model Translator (CH-aware DMT), to reconstruct synthetic SDO/AIA 193 Å EUV images from \HeI{} inputs. The model is trained on temporally co-aligned SOLIS \HeI{} and AIA 193 Å pairs spanning 2011--2015 using a month-based split, where January--October are used for training, November is used for validation, and December for testing. On the held-out test set, the reconstructions preserve dominant full-disk EUV morphology (CC=0.92) and recover CH-related low-intensity structure (CC=0.84). We further assess historical applicability by (1) comparing reconstructed AIA 193 Å morphology with SOHO/EIT 195 Å over 2005--2015; (2) comparing reconstructed AIA 193 Å images generated from KPVT \HeI{} inputs against Yohkoh/SXT soft X-ray observations; and (3) evaluating long-term reconstructed disk-integrated emission statistics against observational EUV series and independent solar activity proxies (sunspot number and F10.7 radio flux over 1974--2015). These results indicate that CH-aware DMT conditioned on \HeI{} can provide a physically plausible synthetic AIA 193 Å coronal proxy for historical studies, supporting multi-decade analyses of large-scale coronal evolution before the direct EUV imaging was available.
In the sciences, regression tasks often require predicting high-dimensional outputs from few training examples. Multi-output Gaussian processes excel in low-data regimes but typically struggle with high-dimensional outputs. Compress-then-predict pipelines such as PCA-GP (principal component analysis plus Gaussian process regression) handle high dimensionality, but rely on bases optimized for reconstruction rather than prediction. To address this gap, we propose a model that represents each output as a linear-Gaussian decoding of a low-dimensional latent state drawn from a Gaussian process prior. By analytically marginalizing the decoder weights, we couple compression and prediction in a single objective that scales to high-dimensional outputs. We refer to this model as Gaussian process latent factor regression (GPLFR). We demonstrate GPLFR by building the first spatially resolved emulator of global climate models for rocky exoplanets.