Kris and Bruce Jenner — SEPARATED

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and Bruce Jenner have separated.

The couple issued a statement saying, “We are living separately and we are much happier this way.”

Sources connected with the family tell our sources … Bruce has been living in Malibu full-time and spending a lot of time with his sons Brody and Brandon.  Kris is firmly planted in Calabasas with her daughters.

We”re told Bruce has privately told his sons living away from Kris was just the way the relationship evolved.

In their statement, they say they will continue to have love and respect for each other.

It”s unclear how the split will impact their reality show.