During Emperor Hadrian's reign, architect and bathhouse engineer Lucius Modestus is troubled by the dismal and densely populated state of Roman baths. One day, while soaking in a bath, he serendipitously uncovers a hidden tunnel that leads him to a contemporary Japanese bathhouse. Initially believing it to be a luxurious retreat for the slaves, he is exhilarated by the modern amenities available, including running water, a beautiful painting of Mount Fuji, and cold beverages, which bring him to tears as he is reminded of his Roman roots. Fueled by inspiration, he decides to incorporate these conveniences into Roman baths.
In a remarkable twist of fate, Lucius finds himself transported to Japan again, this time landing in a private bathroom where he meets Satsuki Odate, a 28-year-old aspiring manga artist. Their accidental encounter, marked by Lucius's mishap with an aerosol can, triggers his return to Rome, leaving him bewildered yet touched. Lucius soon receives an invitation from Hadrian to his villa, where he's commissioned to design a private bath. After another sudden transportation to Satsuki's place of work, a bathroom showroom, Lucius's emotions overflow as he experiences the bliss of an automatic bidet. The jacuzzi he builds for Hadrian impresses the Emperor, showcasing Lucius's talent and burgeoning ideas.
As time progresses, Lucius becomes engulfed in despair when he learns of his wife's infidelity with his closest friend. However, he regains his focus with renewed vigor, returning to Hadrian's service to create a habitat for a Nile crocodile, which the Emperor believes embodies his late lover Antinous. Meanwhile, Satsuki, returning to her hometown after losing her job, brings a Roman coin Lucius had given her to a professor friend, who validates its authenticity and dates a toga Lucius discarded back to the First Century. Satsuki, intrigued by the connection, starts to explore Latin in hopes of understanding more about Lucius.
Hadrian soon reveals his ambition to appoint Ceionius as his heir and commissions Lucius to construct a bath in his honor. While inspecting the site, Lucius encounters hostility from a rival architect, resulting in a fall into a well, which surprisingly transports him back to Satsuki. While she tends to his injuries in an onsen, a romantic moment leads to their mutual transportation back to Rome. Tensions rise as Ceionius attempts to present harassment towards Satsuki, only to be defended by Antoninus. Outraged by Ceionius's actions, Lucius refuses to fulfill Hadrian's demand to build Ceionius a bath, inciting the Emperor's anger.
Satsuki urges Lucius to advise Hadrian to reconsider his choice of heir, suggesting that failure to favor Antoninus would tarnish his reputation as a leader. In light of this, Lucius agrees to create a medical bath along the Danube to aid soldiers, which ultimately rekindles their spirits. Lucius conveys to Hadrian that the idea for the restoration came from Antoninus, preserving the latter's position in succession. As emotions unfold, Satsuki professes her feelings to Lucius, but he does not reciprocate. Nevertheless, he expresses his gratitude for her support, and as Satsuki begins to fade back to her own time, Lucius reassures her that they would reunite, proclaiming that "all roads lead to Rome."
Back in Japan, Satsuki succeeds in pitching a manga series about their experiences to a publisher. As she crosses a bridge in Tokyo, joy radiates from her being as she spots Lucius emerging from the water, signifying a continuation of their extraordinary journey.
