This paper presents the first results from a comparison of Planck dust maps at 353, 545 and 857GHz, along with IRAS data at 3000 (100 μm) and 5000GHz (60 μm), with Green Bank Telescope 21-cm observations of Hi in 14 fields covering more than 800 deg2 at high Galactic latitude. The main goal of this study is to estimate the far-infrared to sub-millimeter (submm) emissivity of dust in the diffuse local interstellar medium (ISM) and in the intermediate-velocity (IVC) and high-velocity clouds (HVC) of the Galactic halo. Galactic dust emission for fields with average Hi column density lower than 2 × 1020 cm-2 is well correlated with 21-cm emission because in such diffuse areas the hydrogen is predominantly in the neutral atomic phase. The residual emission in these fields, once the Hi-correlated emission is removed, is consistent with the expected statistical properties of the cosmic infrared background fluctuations. The brighter fields in our sample, with an average Hi column density greater than 2 × 1020 cm-2, show significant excess dust emission compared to the Hi column density. Regions of excess lie in organized structures that suggest the presence of hydrogen in molecular form, though they are not always correlated with CO emission. In the higher Hi column density fields the excess emission at 857 GHz is about 40% of that coming from the Hi, but over all the high latitude fields surveyed the molecular mass faction is about 10%. Dust emission from IVCs is detected with high significance by this correlation analysis. Its spectral properties are consistent with, compared to the local ISM values, significantly hotter dust (T ~ 20K), lower submm dust opacity normalized per H-atom, and a relative abundance of very small grains to large grains about four times higher. These results are compatible with expectations for clouds that are part of the Galactic fountain in which there is dust shattering and fragmentation. Correlated dust emission in HVCs is not detected; the average of the 99.9% confidence upper limits to the emissivity is 0.15 times the local ISM value at 857 and 3000GHz, in accordance with gas phase evidence for lower metallicity and depletion in these clouds. Unexpected anti-correlated variations of the dust temperature and emission cross-section per H atom are identified in the local ISM and IVCs, a trend that continues into molecular environments. This suggests that dust growth through aggregation, seen in molecular clouds, is active much earlier in the cloud condensation and star formation processes. Corresponding author: M.-A. Miville-Deschênes, e-mail: mamd [at] ias.u-psud.fr (mamd[at]ias[dot]u-psud[dot]fr)