Diddy Denied Bail at Appeal Hearing

5:05 PM PT -- We caught up with Marc Agnifilo outside the courthouse after he made his comments ... and, he tells us Diddy's focused on his defense.

He mentions how poor the conditions in MDC Brooklyn are ... and, says he's working to get Diddy moved to another facility.

3:14 PM PT -- Diddy's attorney Marc Agnifilo is refusing to back down after losing out on their bail appeal hearing, noting to reporters outside the courthouse that their "fight continues."

Per Agnifilo, he's hoping to get Diddy's case to trial sooner rather than later to "minimize" the amount of time he'll have to spend behind bars.

He also called out the rapper's prison conditions as "inhumane" ... though, the lawyer said Diddy is "ready" and "focused" ahead of the trial.

Diddy's fight to get out of jail has stopped in its tracks ... 'cause after arriving at court today to appeal a judge's ruling he shouldn't be released on bail, he's headed back to the detention center.

The rap mogul arrived at a federal courthouse in New York City Wednesday ... where his sons, Christian and Justin, came out to support their dad -- though ultimately, the judge in the case decided not to grant Diddy bail.

U.S. District Judge Andrew Carter -- after hearing arguments from the lawyers -- said he was turning down the request because "the government has proven the defendant is a danger. The bail package is insufficient even on risk of flight."

Assistant U.S. Attorney Emily Johnson mentioned the "Freak Offs" -- sex parties Diddy would allegedly host. She claimed he filmed people having sex with male escorts, partially to use as blackmail.

Johnson says these victims are claiming he drugged them, and then used the tapes he made to extort them as well. Diddy has flatly denied these claims.

She says one such incident occurred on March 5, 2016, when Diddy allegedly tried to force a woman to have sex with an escort ... after which she says Diddy chased down the individual while wearing only a towel -- clearly referring to the hotel surveillance video of Diddy hitting Cassie.

The prosecutor said this alleged incident with Cassie proves Diddy cannot be taken at his word ... and promises the half-dozen sex workers allegedly connected to the case they've found is the "tip of the iceberg."

Johnson's making claims about a series of alleged retaliatory actions as well ... claiming victims' heads were slammed into car windows in order to coerce them into participating.

AUSA Johnson also brings up the prosecution's interest in the guns they allegedly found with their serial numbers removed ... saying this isn't about security but "dangerousness."

She argued Diddy shouldn't be let out on bail because he's allegedly reached out to people involved in the case numerous times -- including singer Kalenna Harper around 128 times.

Diddy's lawyer, Marc Agnifilo, then presented his rebuttal ... presenting the proposed plan from the legal docs they filed early today.

As we told you ... the star -- who's currently jailed at MDC Brooklyn, former home to several notorious stars -- put his bail appeal in writing early today ... proposing he return to his Miami home under the condition he severely restricts which people are allowed to visit him.

He says his security team -- Sage Intelligence -- would hand over visitor logs every night to the government to show exactly who he's contacting ... and, specifically, he offered to restrict female visitors -- with exceptions being family members or mothers of his kids.

Diddy also promised he wouldn't contact known grand jury members. In fact, his lawyers say he won't even have a cell phone, so he wouldn't have been able to contact anyone.

As for how much he was offering, Diddy stuck to his $50 million bail package, secured by his Miami residence and his mother's home.

His lawyers argued Diddy willingly gave up his passport, his family members have given up their passports and he handed over a letter of intent to sell his plane ... so, Diddy's not planning on running from the court, they claimed.

As for employees, Agnifilo says they all handle his finances in California ... so, no one coming in and out of the house.

When it comes to the video of Diddy striking Cassie, Agnifilo said Diddy had a history of drug addiction, which contributed to the incident.

Agnifilo mentioned Governor Andrew Cuomo during his time as well ... saying he engaged in similar conduct to Diddy and wasn't prosecuted. Cuomo was accused of sexual harassment by around a dozen women.

Prosecutors had laid out their case for keeping Diddy in custody without bail Tuesday ... saying they're afraid he'd intimidate witnesses and further obstruct the case if he's released on bond. The prosecutors were also worried Diddy is a flight risk because of his massive financial resources.

Ultimately, Judge Robyn F. Tarnofsky denied bail for Diddy originally ... and, now Carter's done the same.