We map the dust distribution in the central 180″ ( \sim 680 pc ) region of the M31 bulge , based on HST WFC3 and ACS observations in ten bands from near-ultraviolet ( 2700 Å ) to near-infrared ( 1.5 \mu m ) . This large wavelength coverage gives us great leverage to detect not only dense dusty clumps , but also diffuse dusty molecular gas . We fit a pixel-by-pixel spectral energy distributions to construct a high-dynamic-range extinction map with unparalleled angular resolution ( \sim 0.5″ , i.e. , \sim 2 pc ) and sensitivity ( the extinction uncertainty , \delta A _ { V } \sim 0.05 ) . In particular , the data allow to directly fit the fractions of starlight obscured by individual dusty clumps , and hence their radial distances in the bulge . Most of these clumps seem to be located in a thin plane , which is tilted with respect to the M31 disk and appears face-on . We convert the extinction map into a dust mass surface density map and compare it with that derived from the dust emission as observed by Herschel . The dust masses in these two maps are consistent with each other , except in the low-extinction regions , where the mass inferred from the extinction tends to be underestimated . Further , we use simulations to show that our method can be used to measure the masses of dusty clumps in Virgo cluster early-type galaxies to an accuracy within a factor of \sim 2 .