As noted by others, the impedance is quite low so an active solution will be challenging, and is unsuitable if a passive receiver is required for whatever reason.
To match it to say 50Ω, a matching network is required, which effectively either transforms or resonates the capacitance such that it's well damped (or whatever filter spectrum is desired or tolerable) by the transmission line impedance (or internal loss if reduced SNR is acceptable). The far end of which must be terminated to validate that assumption. We cannot rely on device resistance to provide damping (at least, not without a more detailed equivalent circuit -- s params), so this will be a one-port-terminated network, considering the loop between device (photodiode), matching network, cable, and receiver input equivalent (termination).
If this is a baseband/wideband application, then LF or DC, up to some lowpass cutoff, is required. The basic idea is to resonate the capacitance with some inductance, just slightly enough to extend bandwidth, without peaking the response much. We can direct connect it (photodiode straight into transmission line), which gives a cutoff of 530MHz. We can use a series inductor to peak it, extending about 30% or 690MHz. We can use a more complex network to go further, by choosing different prototypes, and increasing filter order (higher order filters extend the band edge slightly, in exchange for steeper stopband attenuation; but returns diminish steeply past 2nd or 3rd order).
Possibly, the capacitive peaking circuit (using T-coils) can be used here, since the source is [largely?] non-resistive: this network is particularly famous for its use by Tektronix engineers in the vacuum tube days, where amplifier inputs and outputs, and CRT deflection inputs, are largely capacitive, and the voltage response is the only thing that matters. Bandwidth can be nearly tripled -- but keep in mind it's purely voltage gain, not power or current gain. As far as I know, power gain can not be extended more than about 40%. I'm not sure about current.
This is still not enough though, so we must compromise by reducing impedance. Matching can then be restored with a narrowband L network, wideband transformer, or baseband resistor (minimum-loss matching attenuator). Evidently, 2.5GHz needs at most 32Ω impedance, but more likely 14Ω or less, at the diode. The SNR budget will be relevant to deciding whether this is acceptable.
Curiously, the goal here is the inverse of traditional peaking (current vs. voltage!); perhaps an inversion of the circuit is possible -- I don't know, I haven't played with that goal. Perhaps not, because the source itself (diode capacitance) cannot be transformed.
References: consider Starič and Margan, Wideband Amplifiers (Springer), especially Part 2: Inductive Peaking Circuits. Other filter design references may be helpful, like Zverev, Handbook of Filter Synthesis, or Williams and Taylor, Electronic Filter Design Handbook (McGraw-Hill). There ought to be papers or books targeting photodiode networks specifically, as well.
