LM317 running digital pulses. Results are Noisy
ICs that differentiate analog and digital ground generally do to to separate 'noisy' power circuitry from 'quiet' analog or digital circuitry. This allows you to keep ground places separated in the layout and allows for a single-point connection between power and signal ground, which is optimal from a noise standpoint.

The LM317 is not a low-dropout type of linear regulator. The attached datasheet has a set of curves on page 7 called "dropout voltage" that illustrates this point:



You're trying to control an output that's within 1 volt of input. The LM317 is not an appropriate choice for this function - it is not regulating anything, as earlier comments have stated.