Liverpool maintained their perfect home record in the Premier League this season, with Diogo Jota and Darwin Nunez scoring quickfire goals in the first half and Mohamed Salah adding a second-half strike.
Liverpool's latest win, their eighth in a row at Anfield in all competitions, was their seventh in ten league games this season and moved them back to within three points of league leaders Tottenham.
Jota held aloft Diaz's number seven shirt after scoring, with the Colombian not featuring in Liverpool's squad following reports his parents had been kidnapped in his homeland.
Forest created few chances and, despite Anthony Elanga hitting the post with a late volley, they were forced to defend for most of the match as their winless league run extended to six games.
A minute's applause was held before kick-off in memory of former England and Manchester United great Sir Bobby Charlton and ex-Everton chairman Bill Kenwright, who both recently died.
Liverpool quickly assumed control, but had only Nunez's angled volley and Jota's header, both easily saved by Forest goalkeeper Matt Turner, to show for all their possession.
But that changed with two goals in four first-half minutes, which gave the half-time scoreline a truer reflection of Liverpool's dominance.
Nunez's fierce first-time shot was parried by Turner into the path of Jota, who turned home the rebound from eight yards.
In celebration, Jota ran to manager Jurgen Klopp, who handed him Diaz's shirt to show to the Liverpool fans.
Nunez doubled Liverpool's lead in the 35th minute with an emphatic near-post finish after Dominik Szoboszlai's cut-back.
Forest's backline looked increasingly vulnerable. Nunez sent an overhead kick narrowly over the crossbar and Turner produced fine saves to deny Ryan Gravenberch and Szoboszlai before the break.
Harvey Elliott went close to a third Liverpool goal soon after stepping off the bench in the second half when his shot was deflected wide by Forest defender Ola Aina.
Salah capitalised on Turner's misjudgement to put Liverpool 3-0 up in the 77th minute.
Turner was caught out by the bounce of Szoboszlai's long diagonal punt up field and Salah raced clear to sidefoot home his eighth league goal of the season.
Forest almost pulled one back in the 85th minute when Elanga's first-time volley following a cross to the far post crashed against the underside of the crossbar.
Liverpool thought they had scored a fourth goal through substitute Cody Gakpo deep in stoppage time, but VAR ruled he had been offside when converting from close range.
