Since his arrest on August 11th last year, Madsen has changed his story on more than one occasion. He initially said that 30-year-old journalist Wall left his homemade submarine, the UC3 Nautilus, at Refshaleøen in Copenhagen on the night of her disappearance. He later said she died after a hatch on the submarine fell on to her head.
In October, he changed his story again, saying Wall was killed by toxic fumes caused by a mechanical fault on the vessel.
That came after Wall's remains - which Madsen has admitted to mutilating by removing the arms, legs and head from the torso - were eventually recovered from the waters of Køge Bay by police divers. There was no evidence of a fracture to the journalist's skull.
Madsen stuck to his most recent version during questioning by police lead prosecutor Jacob Buch-Jepsen on the first day of the 12-day trial on Thursday, which proceeded under intense Danish and international media attention.
In court on Thursday, Madsen said that 30-year-old Wall died when the air pressure suddenly dropped and toxic fumes filled the vessel.
"I'm not interested in much other than Kim Wall's family. I did not want to tell anyone how Kim Wall died," Madsen said at Copenhagen City Court on Thursday according to Ritzau's report.
"I think most people lie to protect others," Madsen also said.
Asked why he kept changing his account, he said his approach at the time was to "stick to my explanation (of an accident) until your evidence means that I have to tell how she died," according to AFP's report from the court.
An autopsy was unable to determine how Wall died, nor has a motive been established.
Denmark's Prosecution service is seeking to prove that Madsen tortured and killed Wall on board the submarine as part of a pre-meditated deviant sexual fantasy.
According to the prosecutor, the 47-year-old amateur engineer brought a saw, sharpened screwdrivers, nylon straps and other implements on board the submarine before sailing into the Øresund waters separating Denmark and Sweden with Wall on August 10th.
He insisted the voyage was not part of a sinister plan and also claimed that Wall, who had agreed to the trip as part of her work on a feature for American magazine Wired, was enjoying herself "until the accident happened".
But the prosecution painted a picture of Madsen as a sexual sadist obsessed with beheadings.
Prosecutors cited a psychological assessment which declared him "a perverted polymorph, and highly sexually deviant".
"He has narcissistic and psychopathic traits, and is manipulating, with a severe lack of empathy and remorse," prosecutor Jakob Buch-Jepsen said, according to AFP.
He said evidence showed Madsen bound Wall by the head, arms and legs before beating her and stabbing her repeatedly in her genital area.
Buch-Jepsen said Madsen then killed her -- probably strangling or slitting her throat -- and cut her up with a saw, stuffing her torso, head, arms and legs in separate bags weighed down with metal objects, and dumping them in Køge Bay.
Madsen admitted to cutting up Wall's body.
He said he sailed around for a few hours, contemplating suicide, and then slept for two hours.
Cutting her up was not a big deal, as he already knew how to amputate limbs "to save lives".
"I don't see how that mattered at that time, as she was dead," Madsen said with a small grin, according to AFP.
"I tried first with an arm, and that went very fast... It went very fast, and I got her out of the submarine."
Prosecutors also introduced as evidence a hard drive seized in his workshop containing fetish films, in which women were tortured, decapitated and burned alive.
Seven texts "about impalement of women, mostly in the genitals" were also found.
Madsen has said the hard drive was not his.
Investigators never found Wall's or Madsen's phones, but were able to recreate some of the messages on them.
On the morning of August 10th, Madsen "googled 'beheaded girl a(r)gony' which leads to a video of an unidentified young woman who is slowly having her throat cut," the prosecutor said.
On July 26th, he also googled "female beheading" and watched the videos.
Asked why he watched the videos, Madsen said: "It is not of a sexual nature. This is about strong emotions. I watch these videos to cry and to feel emotions."
Madsen's defence lawyer Betina Hald Engmark said the prosecution's case didn't hold up.
"If these statements as presented by the prosecutor can be proven, it would be very incriminating for my client. However there is not enough proof," Engmark told the court.
The prosecution has said it will seek a life sentence, which in Denmark averages around 16 years. A verdict is expected on April 25th.