This may be Munch Munch's debut album, but it feels like they've been around for ages. I first saw them play live about four years ago in a horrible, grotty little venue, accompanied by a handful of other people – all of whom, if I remember rightly, were my friends. True to form, Munch Munch divided the group. One scoffed that, "This is real alternative music" (not meant as a compliment). Two more actually walked out because they found the childlike one-note keyboard-playing so ridiculously naïve that they were afraid of collapsing into uproarious laughter. As for me, I was captivated and inspired.

For the uninitiated, Munch Munch were formed in 2006 by Richard Manber and Thomas Carrell, who both studied in Bristol. Loathing to adhere to the standard verse-chorus paradigm, they would weave all sorts of unconnected ideas into their twisted, finger-painted pop songs; one might begin all discordant and Nintendo-esque and shouty, then veer off into a mellifluous ditty. The duo became a four-piece when they took the project live, recruiting Sarah Louise Renwick and Jack O'Connor, and they became known for their dazzling performances.

Between then and now, their sound has undergone a steady and fascinating metamorphosis, finally crystalised in this deftly crafted 40-minute record. In Double Visions the band have honed a more cerebral sound than we've heard before. There is, of course, plenty of continuity with the style previously exhibited in EPs and singles – songs still branch in compelling directions, for example – but they're now more densely constructed and coherent wholes. Munch Munch are using the curious mix of brushes in their palette to create fuller pictures, shirking the private jokes and affected naïvety that populated earlier songs. It's still fun, but it sounds so much bigger, so much more dynamic, layers of Deerhoof-tinged percussion creating an intricate web of rhythms crawling over pulsing bass notes, screaming organs and spiralling mosaics of glock. They remain difficult to categorise: there's noise, but they're not a noise band; there're synths, but this is not synth pop; at times a classic R'n'B vibe seems to take hold, before swinging towards 70s prog. This all creates an air of mystery. But once you begin to unravel the seemingly abstract lyrics, the songs are pregnant with secrets and themes.

The main focus is on growing up and facing adulthood – a perfect narrative for a record keen to flaunt a maturing sound. Its dual perspective is that of post-adolescence (hence, 'Double Visions'): being young, but not as young as you were; not being old, but not so untainted by experience. We have, then, the recognition of increasing temporality in opener 'It's Nothing': "There's nothing happening, but it's the difference that shows…" sings Thomas in his characteristic high-pitched wail, as though marvelling at the changes wrought by the invisible passage of time; it's slow and thoughtful, a splendid forest glittering with golds and silvers like falling leaves. Another part of growing up is overcoming childish pursuits and fears, tackled in the ostensibly juvenile 'Night Corner' and 'Prank Call'. Handled in more depth, 'Wolfman's Wife' takes up the local freak-myth character often seen in teen films: "The head you carefully display to scare away the children, it strikes a terror in me…We ride past your house every night to catch a glimpse of your face." The slow, haunting pace and mood – horror organs, ghostly vocals, stuttering drums – descends halfway through into a maelstrom of keyboards, like thousands of tiny robot fireflies colliding and detonating in bright oranges and yellows. By the more confident, runaway finale, you realise it's about seeing past your fears, even embracing that which frightens.

Progress, then, as you mature. But what of the growing threat of old age, the narrowing of possibilities? "Do you remember when this river ran deeper…a stream that had many tributaries," Thomas and Richard sing to each other in 'River Gleams', the album's finale, which thunders forwards with a kind of terrified euphoria, but invokes togetherness in the face of change: "We grew up together, but our time has come at last/I can't make sense of how these years have passed so quickly." Overall, Double Visions yearns to shed the trepidation between adolescence and adulthood – best captured in 'Bold Man Of The Sea', which uses the metaphor of travelling oceans and stormy waters; subtle shifts in tone and mood suggest the uncertainties of young adulthood, while the lyrics espouse taking risks and seizing opportunities.

As a means of moving on from the band's childlike signature, Double Visions feels like a masterstroke. It reconciles the brilliant colours and shapes of childhood imagination with the stabbing doubts that accompany so-called maturity, the result being a fertile tapestry for you to pick at again and again, discovering something new each time. Granted, it won't please everyone, but compared with the band I saw four years ago, this debut boasts a depth and sophistication demanding more than a cursory look.