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Abstract We make use of sensitive (9.3 μ Jy beam −1 rms) 1.2 mm continuum observations from the Atacama Large Millimeter/submillimeter Array (ALMA) Spectroscopic Survey in the Hubble Ultra-Deep Field (ASPECS) large program to probe dust-enshrouded star formation from 1362 Lyman-break galaxies spanning the redshift range z  = 1.5–10 (to ∼7–28 M ⊙ yr −1 at 4 σ over the entire range). We find that the fraction of ALMA-detected galaxies in our z  = 1.5–10 samples increases steeply with stellar mass, with the detection fraction rising from 0% at 10 9.0 M ⊙ to % at >10 10 M ⊙ . Moreover, on stacking all 1253 low-mass (<10 9.25 M ⊙ ) galaxies over the ASPECS footprint, we find a mean continuum flux of −0.1 ± 0.4 μ Jy beam −1 , implying a hard upper limit on the obscured star formation rate of <0.6 M ⊙ yr −1 (4 σ ) in a typical low-mass galaxy. The correlation between the infrared excess (IRX) of UV-selected galaxies ( L IR / L UV ) and the UV-continuum slope is also seen in our ASPECS data and shows consistency with a Calzetti-like relation at > and an SMC-like relation at lower masses. Using stellar mass and β measurements for z  ∼ 2 galaxies over the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey, we derive a new empirical relation between β and stellar mass and then use this correlation to show that our IRX– β and IRX–stellar mass relations are consistent with each other. We then use these constraints to express the IRX as a bivariate function of β and stellar mass. Finally, we present updated estimates of star formation rate density determinations at z  > 3, leveraging present improvements in the measured IRX and recent probes of ultraluminous far-IR galaxies at z  > 2.