A violent sex offender who was convicted of raping a woman and stomping on her head in a stairwell has been seen on the New South Wales south coast weeks after going on the run.

Key points: Police are on the hunt for two registered sex offenders

Police are on the hunt for two registered sex offenders Violent rapist Christopher William Empey has been missing since November and was last seen on the NSW South Coast

Violent rapist Christopher William Empey has been missing since November and was last seen on the NSW South Coast Child molester Maurice Collie was last seen in Melbourne's CBD just before Christmas

Christopher William Empey was sentenced to at least 12 years' jail in Victoria for the crimes, which left his victim with lifelong injuries.

Empey, of Launceston, met the victim at a work awards night and attacked her in the stairwell of a Southbank apartment block.

She had to learn how to walk and write again.

"It was a particularly horrific and violent offence," said Assistant Commissioner Neil Paterson.

The alarm was raised on November 23 when Empey, 46, failed to comply with his monitoring conditions.

Police believe he was unhappy with a series of new conditions set to be imposed on him.

His GPS monitoring bracelet was found smashed near the Hume Highway.

Investigators believe Empey fled to Nowra in New South Wales where he purchased a motorcycle.

Police only became aware of the sale after government paperwork was lodged.

He was last seen on December 4 when he sold the motorcycle and security footage has emerged of him at a Nowra store, looking unshaven and wearing the same clothes he fled in.

"We believe that he's surviving off the cash that he took from his safe when he disappeared in November," Assistant Commissioner Paterson said.

"We believe he's travelling to avoid apprehension by the police and avoid his obligations for electronic monitoring."

Police said Empey, who is a registered sex offender, is now walking with a limp.

Child sex offender also at-large

Police are also trying to find Maurice Collie, who was convicted in June last year of sexually assaulting an 11-year-old.

Collie, who was last seen at the Salvation Army on Bourke Street in Melbourne before Christmas, failed to contact police after being released from prison on December 17.

It is the fifth time Collie has breached the conditions of his release, the reason he was most recently sent to prison.

Maurice Collie has repeatedly breached his reporting conditions. ( Supplied: Victoria Police )

"Mr Collie is a consistent breacher of his obligations under the Sex Offenders Registration Act and police hold concerns that he may well commit further offences," Assistant Commissioner Paterson said.

"We know that when registered sex offenders are non-compliant with their reporting obligations that their risk increases in terms of committing further offences in the community."

Collie was also convicted in 2016 of sexually penetrating a child under 16.

He also has drug and dishonesty offences.

"Mr Collie is considered a high-risk sex offender and is on the sex offender registry for life," Assistant Commissioner Paterson said.

"For Mr Collie, he pays little attention to his obligations under the act and that therefore increases his risk and increases our concern about him being in the community and not complying with his obligations."

Collie last spoke to his family on Christmas Day and a warrant has been issued for his arrest.

He also goes by Reece Collie or Reece Nelson.

He is known to frequent the Bendigo, Mildura, Geelong, Gippsland, Frankston and Melbourne areas.

Assistant Commissioner Paterson vowed to find both men.

"History shows that when we have missing registered sex offenders or serious offenders, that when we make an appeal to the public, that they are often found within a reasonably short period of time."