diff --git a/.github/workflows/Benchmark.yml b/.github/workflows/Benchmark.yml
new file mode 100644
index 00000000..dfd1e068
--- /dev/null
+++ b/.github/workflows/Benchmark.yml
@@ -0,0 +1,55 @@
+name: Benchmarks
+on:
+  push:
+    branches:
+      - master
+  pull_request:
+    branches:
+      - master
+
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+
+jobs:
+  benchmark:
+    runs-on: ubuntu-latest
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: '1'
+          arch: x64
+      - uses: actions/cache@v4
+        env:
+          cache-name: cache-artifacts
+        with:
+          path: ~/.julia/artifacts
+          key: ${{ runner.os }}-test-${{ env.cache-name }}-${{ hashFiles('**/Project.toml') }}
+          restore-keys: |
+            ${{ runner.os }}-test-${{ env.cache-name }}-
+            ${{ runner.os }}-test-
+            ${{ runner.os }}-
+      - name: Run benchmark
+        run: |
+          cd bench
+          julia --project --threads=2 --color=yes -e '
+            using Pkg;
+            Pkg.develop(PackageSpec(path=joinpath(pwd(), "..")));
+            Pkg.instantiate();
+            include("benchmarks.jl")'
+      - name: Parse & Upload Benchmark Results
+        uses: benchmark-action/github-action-benchmark@v1
+        with:
+          name: Benchmark Results
+          tool: 'julia'
+          output-file-path: bench/benchmark_results.json
+          summary-always: true
+          github-token: ${{ secrets.GITHUB_TOKEN }}
+          comment-always: true
+          alert-threshold: "200%"
+          fail-on-alert: true
+          benchmark-data-dir-path: benchmarks
+          auto-push: ${{ github.event_name != 'pull_request' }}
diff --git a/bench/Project.toml b/bench/Project.toml
new file mode 100644
index 00000000..3cadd820
--- /dev/null
+++ b/bench/Project.toml
@@ -0,0 +1,17 @@
+[deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+AdvancedVI = "b5ca4192-6429-45e5-a2d9-87aec30a685c"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
+Bijectors = "76274a88-744f-5084-9051-94815aaf08c4"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
+DistributionsAD = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
+FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+InteractiveUtils = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
+LogDensityProblems = "6fdf6af0-433a-55f7-b3ed-c6c6e0b8df7c"
+Optimisers = "3bd65402-5787-11e9-1adc-39752487f4e2"
+Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
+ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+SimpleUnPack = "ce78b400-467f-4804-87d8-8f486da07d0a"
+StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
+Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
diff --git a/bench/README.md b/bench/README.md
new file mode 100644
index 00000000..5c5214d8
--- /dev/null
+++ b/bench/README.md
@@ -0,0 +1,7 @@
+
+# AdvancedVI.jl Continuous Benchmarking
+
+This subdirectory contains code for continuous benchmarking of the performance of `AdvancedVI.jl`.
+The initial version was heavily inspired by the setup of [Lux.jl](https://github.com/LuxDL/Lux.jl/tree/main).
+The Github action and pages integration is provided by  https://github.com/benchmark-action/github-action-benchmark/ and [BenchmarkTools.jl](https://github.com/JuliaCI/BenchmarkTools.jl).
+
diff --git a/bench/benchmarks.jl b/bench/benchmarks.jl
new file mode 100644
index 00000000..8585fa8c
--- /dev/null
+++ b/bench/benchmarks.jl
@@ -0,0 +1,60 @@
+
+using ADTypes, ForwardDiff, ReverseDiff, Zygote
+using AdvancedVI
+using BenchmarkTools
+using Bijectors
+using Distributions
+using DistributionsAD
+using FillArrays
+using InteractiveUtils
+using LinearAlgebra
+using LogDensityProblems
+using Optimisers
+using Random
+
+BLAS.set_num_threads(min(4, Threads.nthreads()))
+
+@info sprint(versioninfo)
+@info "BLAS threads: $(BLAS.get_num_threads())"
+
+include("utils.jl")
+include("normallognormal.jl")
+
+const SUITES = BenchmarkGroup()
+
+# Comment until https://github.com/TuringLang/Bijectors.jl/pull/315 is merged
+# SUITES["normal + bijector"]["meanfield"]["Zygote"] =
+#     @benchmarkable normallognormal(
+#         ;
+#         fptype       = Float64,
+#         adtype       = AutoZygote(),
+#         family       = :meanfield,
+#         objective    = :RepGradELBO,
+#         n_montecarlo = 4,
+#     )
+
+SUITES["normal + bijector"]["meanfield"]["ReverseDiff"] =
+    @benchmarkable normallognormal(
+        ;
+        fptype       = Float64,
+        adtype       = AutoReverseDiff(),
+        family       = :meanfield,
+        objective    = :RepGradELBO,
+        n_montecarlo = 4,
+    )
+
+SUITES["normal + bijector"]["meanfield"]["ForwardDiff"] =
+    @benchmarkable normallognormal(
+        ;
+        fptype       = Float64,
+        adtype       = AutoForwardDiff(),
+        family       = :meanfield,
+        objective    = :RepGradELBO,
+        n_montecarlo = 4,
+    )
+
+BenchmarkTools.tune!(SUITES; verbose=true)
+results = BenchmarkTools.run(SUITES; verbose=true)
+display(median(results))
+
+BenchmarkTools.save(joinpath(@__DIR__, "benchmark_results.json"), median(results))
diff --git a/bench/normallognormal.jl b/bench/normallognormal.jl
new file mode 100644
index 00000000..15d5a5a0
--- /dev/null
+++ b/bench/normallognormal.jl
@@ -0,0 +1,56 @@
+
+struct NormalLogNormal{MX,SX,MY,SY}
+    μ_x::MX
+    σ_x::SX
+    μ_y::MY
+    Σ_y::SY
+end
+
+function LogDensityProblems.logdensity(model::NormalLogNormal, θ)
+    (; μ_x, σ_x, μ_y, Σ_y) = model
+    logpdf(LogNormal(μ_x, σ_x), θ[1]) + logpdf(MvNormal(μ_y, Σ_y), θ[2:end])
+end
+
+function LogDensityProblems.dimension(model::NormalLogNormal)
+    length(model.μ_y) + 1
+end
+
+function LogDensityProblems.capabilities(::Type{<:NormalLogNormal})
+    LogDensityProblems.LogDensityOrder{0}()
+end
+
+function Bijectors.bijector(model::NormalLogNormal)
+    (; μ_x, σ_x, μ_y, Σ_y) = model
+    Bijectors.Stacked(
+        Bijectors.bijector.([LogNormal(μ_x, σ_x), MvNormal(μ_y, Σ_y)]),
+        [1:1, 2:1+length(μ_y)])
+end
+
+function normallognormal(; fptype, adtype, family, objective, kwargs...)
+    n_dims = 10
+    μ_x    = fptype(5.0)
+    σ_x    = fptype(0.3)
+    μ_y    = Fill(fptype(5.0), n_dims)
+    σ_y    = Fill(fptype(0.3), n_dims)
+    model  = NormalLogNormal(μ_x, σ_x, μ_y, Diagonal(σ_y.^2))
+
+    obj = variational_objective(objective; kwargs...)
+
+    d = LogDensityProblems.dimension(model)
+    q = variational_standard_mvnormal(fptype, d, family) 
+
+    b             = Bijectors.bijector(model)
+    binv          = inverse(b)
+    q_transformed = Bijectors.TransformedDistribution(q, binv)
+
+    max_iter = 10^3
+    AdvancedVI.optimize(
+        model,
+        obj,
+        q_transformed,
+        max_iter;
+        adtype,
+        optimizer = Optimisers.Adam(fptype(1e-3)),
+        show_progress = false,
+    )
+end
diff --git a/bench/utils.jl b/bench/utils.jl
new file mode 100644
index 00000000..31c87c3d
--- /dev/null
+++ b/bench/utils.jl
@@ -0,0 +1,20 @@
+
+function variational_standard_mvnormal(type::Type, n_dims::Int, family::Symbol)
+    if family == :meanfield
+        AdvancedVI.MeanFieldGaussian(
+            zeros(type, n_dims), Diagonal(ones(type, n_dims))
+        )
+    else
+        AdvancedVI.FullRankGaussian(
+            zeros(type, n_dims), Matrix(type, I, n_dims, n_dims)
+        )
+    end
+end
+
+function variational_objective(objective::Symbol; kwargs...)
+    if objective == :RepGradELBO
+        AdvancedVI.RepGradELBO(kwargs[:n_montecarlo])
+    elseif objective == :RepGradELBOSTL
+        AdvancedVI.RepGradELBO(kwargs[:n_montecarlo], entropy=StickingTheLandingEntropy())
+    end
+end