Better, Faster, Responsive Images for Divi – Upload in Divi child theme.

functions.php

<?php

// enable divi functions
add_action( 'wp_enqueue_scripts', 'my_enqueue_assets' );
function my_enqueue_assets() {
    wp_enqueue_style( 'parent-style', get_template_directory_uri().'/style.css' );
}

//add 1440px image size
add_image_size('image_1440', 1440, 9999, false);


//move the 'wp_make_content_images_responsive' filter to run last
remove_filter( 'the_content', 'wp_make_content_images_responsive', 10);
add_filter( 'the_content', 'wp_make_content_images_responsive', 1600, 1);

add_filter( 'the_content', 'hb_add_id_to_images', 1599, 1);
//filter the content and add wp-image-$id class to the images, allowing responsive feature to work
function hb_add_id_to_images( $content ) {
	global $wpdb;
	if ( ! preg_match_all( '/<img [^>]+>/', $content, $matches ) ) {
		return $content;
	}

	foreach( $matches[0] as $image ) {
		if ( !preg_match( '/wp-image-([0-9]+)/i', $image ) ) {
			$dom = new DOMDocument();
			$dom->loadHTML($image);
			$img_element = $dom->getElementsByTagName('img')->item(0);
			
			$wp_upload_dir = wp_upload_dir();
			$image_path = str_replace(trailingslashit(preg_replace("(^https?://)", "", $wp_upload_dir['baseurl'])), '', preg_replace("(^https?://)", "", $img_element->getAttribute('src') ));
			
			$attachment = $wpdb->get_col($wpdb->prepare("SELECT post_id FROM $wpdb->postmeta WHERE meta_key='_wp_attached_file' AND BINARY meta_value='%s';", $image_path )); 
			
			if ($attachment) {
				$img_element->setAttribute("class", "wp-image-".$attachment[0]);
				$new_image = $img_element->ownerDocument->saveHTML($img_element);
				
				$content = str_replace ( $image , $new_image , $content);
			}
		}
	}

	return $content;
}

//lower image max-width to 1080px everywhere (retina compatible)
function hb_content_image_sizes_attr( $sizes, $size ) {
	$width = $size[0];
	
	if ($width >= 1080) $sizes = '(max-width: 1080px) 100vw, 1080px';

	return $sizes;
}
add_filter( 'wp_calculate_image_sizes', 'hb_content_image_sizes_attr', 10 , 2 );


//override Divi 'et_pb_maybe_add_advanced_styles' function to fix the problem of browser downloading overridden background image
function hb_pb_maybe_add_advanced_styles() {
	$styles = array();

	// do not output advanced css if Frontend Builder is active
	if ( ! et_fb_is_enabled() ) {
		$styles['et-builder-advanced-style'] = ET_Builder_Element::get_style();
		
		if ( preg_match_all('/\.[_a-z0-9]+\.et_pb_fullwidth_header \{.*background-image.*\}/', $styles['et-builder-advanced-style'], $matches ) ) {
			foreach( $matches[0] as $bg_css ) {
				$styles['et-builder-advanced-style'] = preg_replace('/url\(.*\)/', 'none', $styles['et-builder-advanced-style']);
			}
		}
				
		$styles['et-builder-page-custom-style'] = et_pb_get_page_custom_css();
	}

	foreach( $styles as $id => $style_data ) {
		if ( ! $style_data ) {
			continue;
		}

		printf(
			'<style type="text/css" id="%2$s">
				%1$s
			</style>',
			$style_data,
			esc_attr( $id )
		);
	}
	
	remove_action( 'wp_footer', 'et_pb_maybe_add_advanced_styles' );
}
add_action( 'wp_footer', 'hb_pb_maybe_add_advanced_styles', 9 );


add_action('wp_footer', 'hb_responsive_bg_image', 10);
//add responsiveness for background images
function hb_responsive_bg_image() {
	global $wpdb;
	
	$css = ET_Builder_Element::get_style();


	//find the background-image css in the inline css	
	if ( preg_match_all('/\.[_a-z0-9]+\.et_pb_fullwidth_header \{.*background-image.*\}/', $css, $matches ) ) {
		foreach( $matches[0] as $bg_css ) {
			if (preg_match('/\b(?:(?:https?|ftp|file):\/\/|www\.|ftp\.)[-A-Z0-9+&@#\/%=~_|$?!:,.]*[A-Z0-9+&@#\/%=~_|$]/i', $bg_css, $url_matches)) {
				$url = $url_matches[0];
				
				$wp_upload_dir = wp_upload_dir();
				
				
				$image_path = str_replace(trailingslashit(preg_replace("(^https?://)", "", $wp_upload_dir['baseurl'])), '', preg_replace("(^https?://)", "", $url ));
				
				$attachment = $wpdb->get_col($wpdb->prepare("SELECT post_id FROM $wpdb->postmeta WHERE meta_key='_wp_attached_file' AND BINARY meta_value='%s';", $image_path )); 
				
				$bg_css = preg_replace('/background-color([^;]*);/', '', $bg_css, 1);
				
				if ($attachment) {
					$image_meta = wp_get_attachment_metadata($attachment[0]);
					
					$extra_css = '';


					//add fullsize background image style, fixing the problem of browser downloading overridden background image
					$extra_css .= '
						@media only screen and ( min-width: 1441px ) {
							' . $bg_css . '
						}';
					
					//add responsive background image for (non-retina) screen with max-width 1440px (use 1440px image), 1080px (use 1080px image), 768px (use 768px image)
					if ($image_meta['sizes']['image_1440']) {
						$extra_css .= '
						@media only screen and ( max-width: 1440px ) {
							' . str_replace(basename($url), $image_meta['sizes']['image_1440']['file'], $bg_css) . '
						}';
					}

					if ($image_meta['sizes']['et-pb-portfolio-image-single']) {
						$extra_css .= '
						@media only screen and ( max-width: 1080px ) {
							' . str_replace(basename($url), $image_meta['sizes']['et-pb-portfolio-image-single']['file'], $bg_css) . '
						}';
					}
					
					if ($image_meta['sizes']['medium_large']) {
						$extra_css .= '
						@media only screen and ( max-width: 768px ) {
							' . str_replace(basename($url), $image_meta['sizes']['medium_large']['file'], $bg_css) . '
						}';
					}
					
					
					//add responsive background image for retina screen with max-width 1440px (use fullsize image), 768px (use 1440px image), 540px (use 1080px image), 384px (use 768px image)
					$extra_css .= '
					@media
					only screen and ( max-width: 1440px ) and (-webkit-min-device-pixel-ratio: 2),
					only screen and ( max-width: 1440px ) and (   min--moz-device-pixel-ratio: 2),
					only screen and ( max-width: 1440px ) and (     -o-min-device-pixel-ratio: 2/1),
					only screen and ( max-width: 1440px ) and (        min-device-pixel-ratio: 2),
					only screen and ( max-width: 1440px ) and (                min-resolution: 192dpi),
					only screen and ( max-width: 1440px ) and (                min-resolution: 2dppx) { 
						' . $bg_css . '
					}';

					if ($image_meta['sizes']['image_1440']) {
						$extra_css .= '
						@media
						only screen and ( max-width: 768px ) and (-webkit-min-device-pixel-ratio: 2),
						only screen and ( max-width: 768px ) and (   min--moz-device-pixel-ratio: 2),
						only screen and ( max-width: 768px ) and (     -o-min-device-pixel-ratio: 2/1),
						only screen and ( max-width: 768px ) and (        min-device-pixel-ratio: 2),
						only screen and ( max-width: 768px ) and (                min-resolution: 192dpi),
						only screen and ( max-width: 768px ) and (                min-resolution: 2dppx) { 
							' . str_replace(basename($url), $image_meta['sizes']['image_1440']['file'], $bg_css) . '
						}';
					}

					if ($image_meta['sizes']['et-pb-portfolio-image-single']) {
						$extra_css .= '
						@media
						only screen and ( max-width: 540px ) and (-webkit-min-device-pixel-ratio: 2),
						only screen and ( max-width: 540px ) and (   min--moz-device-pixel-ratio: 2),
						only screen and ( max-width: 540px ) and (     -o-min-device-pixel-ratio: 2/1),
						only screen and ( max-width: 540px ) and (        min-device-pixel-ratio: 2),
						only screen and ( max-width: 540px ) and (                min-resolution: 192dpi),
						only screen and ( max-width: 540px ) and (                min-resolution: 2dppx) { 
							' . str_replace(basename($url), $image_meta['sizes']['et-pb-portfolio-image-single']['file'], $bg_css) . '
						}';
					}

					if ($image_meta['sizes']['medium_large']) {
						$extra_css .= '
						@media
						only screen and ( max-width: 384px ) and (-webkit-min-device-pixel-ratio: 2),
						only screen and ( max-width: 384px ) and (   min--moz-device-pixel-ratio: 2),
						only screen and ( max-width: 384px ) and (     -o-min-device-pixel-ratio: 2/1),
						only screen and ( max-width: 384px ) and (        min-device-pixel-ratio: 2),
						only screen and ( max-width: 384px ) and (                min-resolution: 192dpi),
						only screen and ( max-width: 384px ) and (                min-resolution: 2dppx) { 
							' . str_replace(basename($url), $image_meta['sizes']['medium_large']['file'], $bg_css) . '
						}';
					}
					
					?>
					<style type="text/css" id="responsive-bg-image-style">
					<?php echo $extra_css;?>
					</style>
					<?php
				}
			}
		}
	}
}
// **********End Faster, Better Divi images******

With the new version 2.27 of the Divi / Extra Theme SRCSET is support, hooray!!! :-)
https://www.elegantthemes.com/api/changelog/extra.txt

version 2.27 ( updated 08-15-2019 )

• Added SRCSET support for responsive images.

With the new version 2.27 of the Divi / Extra Theme SRCSET is support, hooray!!! :-)
https://www.elegantthemes.com/api/changelog/extra.txt

version 2.27 ( updated 08-15-2019 )

• Added SRCSET support for responsive images.

Yes, but still no background image optimization. So the second part should be still useful for page speed improvements.

While i can't get this to work anymore i found a promising plugin called Optimole:
https://wordpress.org/plugins/optimole-wp/

It's free for websites that stay under 5000 unique views per month. It serves all images INCLUDING background images via their CDN and makes them responsive and as a bonus converts them to webp.

This drastically improved my pagespeed score, getting rid of anything regarding images :)