Michael Madsen‘s sons are gathering outside his Malibu home where he was found dead … the emotions are coming out, and it’s all on video.

The ‘Kill Bill’ actor’s four sons — Christian, Max, Luke and Kalvin — hugged and embraced Tuesday at their father’s estate … and they look somber and sad.

As we reported … Michael was found dead inside the house Thursday morning after someone called 911 to report him unresponsive. LASD deputies arrived and pronounced Michael dead at the scene.

Michael’s death is sending shockwaves through Hollywood and his actress sister Virginia Madsen and others he worked with are sharing fond memories and heartfelt tributes … including Vivica A. Fox and Jennifer Tilly.

The official cause of death is unclear, but law enforcement sources tell us no foul play is suspected and it appears he died from natural causes. Michael’s rep Liz Rodriguez tells us he suffered cardiac arrest.