Beneath the very public collapse of Adidas AG’s multibillion-dollar sneaker deal with Ye is a private legal battle over a $100 million-a-year marketing fund.

The fund, from which Adidas claims the rapper diverted $75 million, has come to the fore as the two sides trade accusations behind closed doors over the partnership that imploded last year, sending the German apparel maker reeling.

Details of the dispute, which is being conducted through an arbitrator, had been closely guarded until they were accidentally revealed in a related hearing in May, when the parties’ lawyers discussed them in open court. Bits and pieces of the conflict have also been seeping out in legal filings, including one in which Adidas alleges that the hiphop artist formerly known as Kanye W…