DiagNormal is substantially slower than Product of Normals

[penelopeysm]

Distributions.jl/src/product.jl

Lines 239 to 250 in abb151c

	"""
	product_distribution(dists::AbstractVector{<:Normal})
	Create a multivariate normal distribution by stacking the univariate normal distributions.
	The resulting distribution of type [`MvNormal`](@ref) has a diagonal covariance matrix.
	"""
	function product_distribution(dists::AbstractVector{<:Normal})
	µ = map(mean, dists)
	σ2 = map(var, dists)
	return MvNormal(µ, Diagonal(σ2))
	end

product_distribution on an array of Normals creates a DiagNormal. That's actually quite satisfying to look at, but the original Product is quite substantially faster:

julia> using Distributions, Chairmarks

julia> dists = [Normal(0.0), Normal(1.0), Normal(2.0, 3.0), Normal(4.0, 0.2)];

julia> prod = Product(dists);

julia> mvnorm = product_distribution(dists);

rand

julia> @be rand($prod)
Benchmark: 3556 samples with 805 evaluations
 min    23.034 ns (2 allocs: 96 bytes)
 median 24.845 ns (2 allocs: 96 bytes)
 mean   33.334 ns (2 allocs: 96 bytes, 0.25% gc time)
 max    5.135 μs (2 allocs: 96 bytes, 98.75% gc time)

julia> @be rand($mvnorm)
Benchmark: 8044 samples with 260 evaluations
 min    32.212 ns (2 allocs: 96 bytes)
 median 34.935 ns (2 allocs: 96 bytes)
 mean   42.677 ns (2 allocs: 96 bytes, 0.07% gc time)
 max    13.362 μs (2 allocs: 96 bytes, 98.83% gc time)

logpdf

julia> x = rand(prod)
4-element Vector{Float64}:
  1.7947570646417756
  1.050115051070052
 -1.0885138050761758
  4.265595405348341

julia> @be logpdf($prod, $x)
Benchmark: 3290 samples with 1220 evaluations
 min    23.498 ns
 median 23.599 ns
 mean   23.693 ns
 max    44.125 ns

julia> @be logpdf($mvnorm, $x)
Benchmark: 2827 samples with 464 evaluations
 min    61.332 ns (2 allocs: 96 bytes)
 median 62.409 ns (2 allocs: 96 bytes)
 mean   71.665 ns (2 allocs: 96 bytes, 0.14% gc time)
 max    9.668 μs (2 allocs: 96 bytes, 98.51% gc time)

Similar performance differences are observed when taking the gradient of logpdf.

Perhaps there are some performance improvements that can be done for DiagNormal?

repro

(ppl) pkg> st
Status `~/ppl/Project.toml`
  [0ca39b1e] Chairmarks v1.3.1
  [31c24e10] Distributions v0.25.120

julia> versioninfo()
Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 10 × Apple M1 Pro
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 8 virtual cores)