Demon Slayer – Kimetsu No Yaiba – The Movie: Mugen Train will receive a seven-episode television anime version in Japan titled Kimetsu no Yaiba: Mugen Train Arc. It will premiere on October 10.
Crunchyroll and Funimation also announced that they will stream the television anime version, which is meant to connect the Demon Slayer: Kimetsu No Yaiba series’ Tanjiro Kamado, Unwavering Resolve Arc with the with the upcoming second season’s Entertainment District Arc.
The TV recut version of Mugen Train will add “around 70” new cuts and additional background music, as well as the opening song “Akeboshi” and the ending song “Shirogane” by LiSA. Additionally, the first episode will depict Kyōjurō Rengoku’s experiences between his departure from the Demon Slayer Corps’ headquarters and his arrival at the Infinity Train.

The Mugen Train movie was released in Japan in October 2020. It is the top-grossing movie in Japan as well as the highest-grossing movie of 2020 worldwide.
Mugen Train is a sequel to the Demon Slayer -Kimetsu no Yaiba- anime series, which aired in 2019 with 26 episodes and is set to receive a second season in 2021. Both are based on the manga by Koyoharu Gotōge, which was first serialized in 2016 in the Weekly Shonen Jump magazine and ended with 211 chapters in 2020 with a total of 23 tankōbon volumes published.
Aniplex of America describes the first season as:
It is the Taisho Period in Japan. Tanjiro, a kindhearted boy who sells charcoal for a living, finds his family slaughtered by a demon. To make matters worse, his younger sister Nezuko, the sole survivor, has been transformed into a demon herself. Though devastated by this grim reality, Tanjiro resolves to become a “demon slayer” so that he can turn his sister back into a human, and kill the demon that massacred his family.
Meanwhile, Funimation describes Mugen Train as:
Falling forever into an endless dream…
Tanjiro and the group have completed their rehabilitation training at the Butterfly Mansion, and they arrive to their next mission on the Mugen Train, where over 40 people have disappeared in a very short period of time.
Tanjiro and Nezuko, along with Zenitsu and Inosuke, join one of the most powerful swordsmen within the Demon Slayer Corps, Flame Hashira Kyojuro Rengoku, to face the demon aboard the Mugen Train on track to despair.
Source: Kimetsu no Yaiba Twitter