Matt Damon and Emily Blunt fall in love and flee shadowy figures in the immensely stylish romantic thriller The Adjustment Bureau. If only the ending lived up to the build-up.

Damon and Blunt have crazy, sexy chemistry from the very first moment they meet, in the gleaming men’s room of the Waldorf Astoria Hotel, of all places. They’re a real treat to watch together — he’s reserved and sort of smart-alecky, she’s quick-witted and flirty — and the contrast in their appearances and personalities just works.

You want them to end up with each other, despite the many elaborate and creative obstacles that thrust themselves in the couple’s path over several years and across New York City’s five boroughs. With all that heat and hype, you long for a climax worthy of the dedication their characters (and the actors) have given.

Instead, writer-director George Nolfi’s film takes all that dazzle and wraps things up with a fizzle: Following intelligent debates about the nature of free will, The Adjustment Bureau ends in an overly simplistic, heavy-handed religious allegory that leaves you wondering, really? Is that it? That it’s based on a short story by Philip K Dick, whose writing has been the inspiration for such groundbreaking sci-fi films as Blade Runner and Minority Report, represents even more of a letdown. Dick’s dark, paranoid vision sadly goes soft.

But it’s got a lot going for it, for a while. The Adjustment Bureau is shot beautifully, the stark cinematography from Oscar-winner John Toll reflecting the isolation and frustration Damon’s character feels.

Damon stars as David Norris, a young and up-and-coming congressman who’s on the verge of losing his bid for the US Senate at the film’s start. While practicing his concession speech in the men’s bathroom, where he thinks he’s alone, he runs into Blunt’s character, Elise. He’s a kid who grew up without much family in a rough part of Brooklyn; she’s a sophisticated, British ballet dancer. But their attraction is palpable; they kiss impetuously, and then she runs off.

David’s instantly, and understandably, smitten. But as it turns out, that was the only time he was ever supposed to see Elise. His life — and all our lives, according to the film — are managed by The Adjustment Bureau, men in tailored suits and fedoras who make sure everyone and everything follows a predetermined plan. If anyone steps out of line by accident, a little nudge here or there steers things back to their proper course.

When David learns from Richardson, (played with perfect, Mad Men-style cool by John Slattery), one of the man adjusters assigned to his case, that he and Elise can never be together, he’s naturally more inspired than ever to track her down. Anthony Mackie is his usual charismatic self as another bureau member, who’s a little more sympathetic to David’s cause, while Terence Stamp makes a huge impression in just a few scenes, as always, as a far more rigid enforcer. (In case you hadn’t noticed, it’s an excellent cast.)

And so David and Elise hook up and go on the run, using the Adjustment Bureau’s own tricks for being everywhere and seeing everything all at once. Yes, this involves wearing silly, magical hats and running through myriad, secret doors, but it also makes exciting leaps in time and space — and asks us to do the same — as the couple dashes from one portal to the next through hidden passageways all over New York City. One second they may be at the foot of the Statue of Liberty; next, they’re in the outfield at Yankee Stadium. It’s reminiscent of “Inception” in its striking visuals and the assumptions it requires us to make, but it moves so fluidly, and it’s in the name of a love that seems so perfect, you may as well give in.

But that’s right about when you’ll get your heart broken. We won’t give too much away. But after raising intriguing philosophical questions about determinism, The Adjustment Bureau gives into the saddest, softest fate of all. David and Elise — and we as viewers — deserve more. And we should be able to choose it for ourselves.