  Accurately quantifying the impact of radiation feedback in star formation is
challenging. To address this complex problem, we employ deep learning
techniques, denoising diffusion probabilistic models (DDPMs), to predict the
interstellar radiation field (ISRF) strength based on three-band dust emission
at 4.5 \um, 24 \um, and 250 \um. We adopt magnetohydrodynamic simulations from
the STARFORGE (STAR FORmation in Gaseous Environments) project that model star
formation and giant molecular cloud (GMC) evolution. We generate synthetic dust
emission maps matching observed spectral energy distributions in the Monoceros
R2 (MonR2) GMC. We train DDPMs to estimate the ISRF using synthetic three-band
dust emission. The dispersion between the predictions and true values is within
a factor of 0.1 for the test set. We extended our assessment of the diffusion
model to include new simulations with varying physical parameters. While there
is a consistent offset observed in these out-of-distribution simulations, the
model effectively constrains the relative intensity to within a factor of 2.
Meanwhile, our analysis reveals weak correlation between the ISRF solely
derived from dust temperature and the actual ISRF. We apply our trained model
to predict the ISRF in MonR2, revealing a correspondence between intense ISRF,
bright sources, and high dust emission, confirming the model's ability to
capture ISRF variations. Our model robustly predicts radiation feedback
distribution, even in complex, poorly constrained ISRF environments like those
influenced by nearby star clusters. However, precise ISRF predictions require
an accurate training dataset mirroring the target molecular cloud's unique
physical conditions.
