Current Code

    <?php
        $parent = get_cat_ID("photos");
        $cats = get_categories("child_of=".$parent);
        foreach ($cats as $cat) {
        query_posts("posts_per_page=1&orderby=rand&cat=".$cat->term_id);
    ?>
        <?php if ( have_posts() ) : while ( have_posts() ) : the_post(); ?>
            <ul>
                <?php if (has_post_thumbnail()) { ?>
                    <?php
                        printf( '<li><a href="'.get_category_link($cat->term_id).'">'.get_the_post_thumbnail(get_the_ID(), "album-thumb").'</a><a href="'.get_category_link($cat->term_id).'">%s</a></li>',
                        apply_filters('get_term', $cat->name));
                    ?>
                <?php } ?>
            </ul>
        <?php endwhile; else: ?>
            <p><?php _e("Sorry, no posts matched your criteria."); ?></p>
        <?php endif; } ?>
    <?php wp_reset_query(); ?>