If approved, the 100-page "family code" would put Cuba at the vanguard of progressive social policy in Latin America, legalising same-sex marriage and civil unions, allowing same-sex couples to adopt children and promoting equal sharing of domestic rights and responsibilities between men and women.
President Miguel Diaz-Canel, who walked with his wife to vote just a few blocks from their home in the Havana suburb of Siboney, told reporters the code abolishes prejudices and taboos that have been ingrained in Cuban society.
"My expectation is that most of the population will vote 'yes'," Diaz-Canel said.
"But regardless of whether 'yes' or 'no' wins... the popular debate that has been generated has contributed to our society."
The code, which has undergone 25 drafts, nearly 80,000 townhall-style meetings and 300,000 suggestions from the public, is expected to draw millions of Cubans to the polls.Â
The measure requires more than 50 per cent of votes cast on Sunday to become law.
Most prior ballot initiatives in Cuba have been overwhelmingly approved but an economic crisis that has led to long lines for food, medicine and fuel has raised the possibility of a protest vote against the government.
"We have to get used to the fact that on such complex issues, where there is a diversity of criteria... there may be people who vote to punish (the government)," Diaz-Canel said.
"That is also legitimate."
Sunday's vote will be the first of its kind since mobile internet was legalised in 2018, which has let dissenting views spread more widely.
There are no independent outside observers of Cuban elections but citizens may observe the count at their precincts immediately following the vote.
The government flooded TV and radio in recent weeks with spots celebrating diversity and inclusion to promote the code.
"This code makes everyone equal," said Jose Antonio Fernandez, a 73-year-old retired Havana resident who voted in favour of the measure on Sunday morning.
Some social conservatives - including the Roman Catholic Church and evangelicals, see things differently, objecting to issues including gay marriage and complaining that government control of the media has drowned out opposing views.
Havana resident Lisandra Samon, 36, said she voted on Sunday but thought it was hard to predict the outcome.
"The vote will be close... aspects of this code have divided the opinions of the public, even families," she said.
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