Display the post date. Only output the date if the current post’s date is different from the previous one output (like the_date).
Use the_date for yesterday or older.
Use “Today” for today, but only for the first post of the day (same behaviour as the_date).
<?php
$latest_query = new WP_query( $args );
...
//inside the loop:
$today = date('Y-m-d');
$published_date = get_the_date( 'Y-m-d' );
if ( $published_date < $today ) { the_date(); } elseif ( $published_date == $today && $latest_query->current_post == 0) { echo 'Today'; } ?>