Throughout the discussion of the Metzorah, the Rishonim make note of the similarity between it and the Parah Adumah and it and the goat sent to Azazel on Yom Kippur. Like the Parah Adumah, cedar wood, crimson wool and hyssop is used in the service. Additionally, the impurity periods last for seven day increments with regard to both the Metzorah and the one who is purifying via the Parah Adumah. Rabbeinu Bachye also compares the following aspect: the Parah Adumah makes the impure pure and the pure impure, tzaraas has the same effect. If one were impure due to tzaraas and then it spread to his entire body he becomes pure due to the tzaraas. The Metzorah's sacrifices are like those of the goat sent on Yom Kippur as both this goat and the bird that is sent away are not offered in the Temple rather they are sent to a distance. They both also have a companion that is offered in the Temple.
The Parah Adumah and the goat sent to Azazel are considered to have similar meaning the Ramban mentions that both symbolize our purification from the evil forces associated with Eisav and Mars. The goat is sent to the vast wilderness and appears as if it is coming to appease the evil force of Mars which is considered to have affect over this region. The Parah Adumah is red and this color is symbolic of the red planet and the goat is symbolic of the se'irim (demons) that are considered to be controlled by the planet Mars. All these ideas of the underworld and death (for which the Parah purifies) are considered to be the domain of Eisav.
Rabbeinu Bachye points out that the Metzorah's sacrifices are coming for this same idea but not as extreme. The bird is sent away, but not all the way to the wilderness. Perhaps, this concept is expressed by the fact that the impurity for which the Metzorah is receiving forgiveness is not as extreme as death itself. It is for tzaraas which makes the individual separate from humanity and renders him like he is dead, but he is not physically dead.
Interestingly, there are two planets that are considered to have evil influence. The first is Mars and that is the one mentioned with Parah Adumah and the goat of Yom Kippur. The other is Saturn. Saturn is associated with all sorts of physical ailments and the Ibn Ezra specifies tzaraas specifically with regard to this planet. (See Reishis Chachma) Perhaps, these purification processes display the prescribed service to free oneself of the influences of these malevolent planets.