As there is no positive proof that Acta Diurna relating to the trial of Jesus ever existed, the options are i) we do not know, or ii) they did not exist. The first of these options is generally unhelpful, but I believe I can show that they almost certainly did not exist - bearing in mind that it is considered almost impossible to prove a negative conclusively.
If there were any contemporary Roman record of the trial of Jesus or of any other aspect in his life, we can be sure that this would be carefully preserved, to become one of the best known and most cited record in the Christian faith. Of course, to the Romans, Jesus would have been a minor criminal on the fringe of empire and it would be hardly worth making records of his life and crucifixion. We ought not be surprised that Roman records do not exist, and their absence proves nothing about the historicity of Jesus.
The best proof that Roman records of Jesus did not exist is the pseudepigraphical Acts of Pilate, written in the second century, allegedly providing a report of the Roman procurator concerning Jesus. Had a true record existed at that time, then the Acts of Pilate would probably not have been written. Further evidence is that Justin Martyr cited the Acts of Pilate, the only 'Roman record' known to him. The Report of Pilate to the Emperor Claudius is another pseudepigraphical document found in the Greek Acts of Peter and Paul and as an appendix to the Gospel of Nicodemus in Latin. The Report of Pilate would appear to be older than the documents into which it had been inserted and is evidence that a true record did not then exist.
As a protege of Emperor Flavius, the first-century Jewish historian, Josephus had access to Roman records and would surely have mentioned the life and crucifixion of Jesus if Jesus had a momentous impact on Jewish society, since he reported on several other revolutionaries and false messiahs who preceded Jesus. Josephus does mention Jesus in two passages, but only in regard to Christian beliefs about Jesus. Because of these two passages, which provided a tenuous link back to Jesus, the works of Josephus were preserved, although not in autograph.
Bishop John Shelby Spong researched the gospel account of Barabbas and says, in Jesus for the NonReligious, at page 168, that has he been able to find no evidence that there was a custom of releasing a prisoner at the time of the Passover.
No Roman record of Jesus is known to have existed; the evidence of history is that such a record probably did not exist.