diff --git a/src/multivariate/dirichlet.jl b/src/multivariate/dirichlet.jl
index b24980ec9..9750d4047 100644
--- a/src/multivariate/dirichlet.jl
+++ b/src/multivariate/dirichlet.jl
@@ -156,18 +156,57 @@ end
 
 function _rand!(rng::AbstractRNG,
                 d::Union{Dirichlet,DirichletCanon},
-                x::AbstractVector{<:Real})
-    for (i, αi) in zip(eachindex(x), d.alpha)
-        @inbounds x[i] = rand(rng, Gamma(αi))
+                x::AbstractVector{E}) where {E<:Real}
+    
+    if any(a -> a >= .5, d.alpha)
+        for (i, αi) in zip(eachindex(x), d.alpha)
+            @inbounds x[i] = rand(rng, Gamma(αi))
+        end
+
+        return lmul!(inv(sum(x)), x)
+    else
+        # Sample in log-space to lower underflow risk
+        for (i, αi) in zip(eachindex(x), d.alpha)
+            @inbounds x[i] = _logrand(rng, Gamma(αi))
+        end
+
+        if all(isinf, x)
+            # Final fallback, parameters likely deeply subnormal
+            # Distribution behavior approaches categorical as Σα -> 0
+            p = copy(d.alpha)
+            p .*= floatmax(eltype(p)) # rescale to non-subnormal
+            x .= zero(E)
+            x[rand(rng, Categorical(inv(sum(p)) .* p))] = one(E)
+            return x
+        end
+
+        return softmax!(x)
     end
-    lmul!(inv(sum(x)), x) # this returns x
 end
 
 function _rand!(rng::AbstractRNG,
                 d::Dirichlet{T,<:FillArrays.AbstractFill{T}},
-                x::AbstractVector{<:Real}) where {T<:Real}
-    rand!(rng, Gamma(FillArrays.getindex_value(d.alpha)), x)
-    lmul!(inv(sum(x)), x) # this returns x
+                x::AbstractVector{E}) where {T<:Real, E<:Real}
+    
+    if FillArrays.getindex_value(d.alpha) >= 0.5
+        rand!(rng, Gamma(FillArrays.getindex_value(d.alpha)), x)
+        return lmul!(inv(sum(x)), x)
+    else
+        # Sample in log-space to lower underflow risk
+        _logrand!(rng, Gamma(FillArrays.getindex_value(d.alpha)), x)
+        
+        if all(isinf, x)
+            # Final fallback, parameters likely deeply subnormal
+            # Distribution behavior approaches categorical as Σα -> 0
+            n = length(d.alpha)
+            p = Fill(inv(n), n)
+            x .= zero(E)
+            x[rand(rng, Categorical(p))] = one(E)
+            return x
+        end
+
+        return softmax!(x)
+    end
 end
 
 #######################################
diff --git a/src/samplers.jl b/src/samplers.jl
index 794f2bff4..988fe5cd2 100644
--- a/src/samplers.jl
+++ b/src/samplers.jl
@@ -20,6 +20,7 @@ for fname in ["aliastable.jl",
               "poisson.jl",
               "exponential.jl",
               "gamma.jl",
+              "expgamma.jl",
               "multinomial.jl",
               "vonmises.jl",
               "vonmisesfisher.jl",
diff --git a/src/samplers/expgamma.jl b/src/samplers/expgamma.jl
new file mode 100644
index 000000000..3fefbb3a4
--- /dev/null
+++ b/src/samplers/expgamma.jl
@@ -0,0 +1,86 @@
+# These are used to bypass subnormals when sampling from
+
+# Inverse Power sampler
+# uses the x*u^(1/a) trick from Marsaglia and Tsang (2000) for when shape < 1
+struct ExpGammaIPSampler{S<:Sampleable{Univariate,Continuous},T<:Real} <: Sampleable{Univariate,Continuous}
+    s::S #sampler for Gamma(1+shape,scale)
+    nia::T #-1/scale
+end
+
+ExpGammaIPSampler(d::Gamma) = ExpGammaIPSampler(d, GammaMTSampler)
+function ExpGammaIPSampler(d::Gamma, ::Type{S}) where {S<:Sampleable}
+    shape_d = shape(d)
+    sampler = S(Gamma{partype(d)}(1 + shape_d, scale(d)))
+    return GammaIPSampler(sampler, -inv(shape_d))
+end
+
+function rand(rng::AbstractRNG, s::ExpGammaIPSampler)
+    x = log(rand(rng, s.s))
+    e = randexp(rng, typeof(x))
+    return muladd(s.nia, e, x)
+end
+
+
+# Small Shape sampler
+# From Liu, C., Martin, R., and Syring, N. (2015) for when shape < 0.3
+struct ExpGammaSSSampler{T<:Real} <: Sampleable{Univariate,Continuous}
+    α::T
+    θ::T
+    λ::T
+    ω::T
+    ωω::T
+end
+
+function ExpGammaSSSampler(d::Gamma)
+    α = shape(d)
+    ω = α / MathConstants.e / (1 - α)
+    return ExpGammaSSSampler(promote(
+        α,
+        scale(d),
+        inv(α) - 1,
+        ω,
+        inv(ω + 1)
+    )...)
+end
+
+function rand(rng::AbstractRNG, s::ExpGammaSSSampler{T})::Float64 where T
+    flT = float(T)
+    while true
+        U = rand(rng, flT)
+        z = (U <= s.ωω) ? -log(U / s.ωω) : log(rand(rng, flT)) / s.λ
+        h = exp(-z - exp(-z / s.α))
+        η = z >= zero(T) ? exp(-z) : s.ω * s.λ * exp(s.λ * z)
+        if h / η > rand(rng, flT)
+            return s.θ - z / s.α
+        end
+    end
+end
+
+
+function _logsampler(d::Gamma)
+    if shape(d) < 0.3
+        return ExpGammaSSSampler(d)
+    else
+        return ExpGammaIPSampler(d)
+    end
+end
+
+function _logrand(rng::AbstractRNG, d::Gamma)
+    if shape(d) < 0.3
+        return rand(rng, ExpGammaSSSampler(d))
+    else
+        return rand(rng, ExpGammaIPSampler(d))
+    end
+end
+
+function _logrand!(rng::AbstractRNG, d::Gamma, A::AbstractArray{<:Real})
+    if shape(d) < 0.3
+        @inbounds for i in eachindex(A)
+            A[i] = rand(rng, ExpGammaSSSampler(d))
+        end
+    else
+        @inbounds for i in eachindex(A)
+            A[i] = rand(rng, ExpGammaIPSampler(d))
+        end
+    end
+end
diff --git a/test/multivariate/dirichlet.jl b/test/multivariate/dirichlet.jl
index 78de162dc..6da49bf1a 100644
--- a/test/multivariate/dirichlet.jl
+++ b/test/multivariate/dirichlet.jl
@@ -158,3 +158,29 @@ end
         end
     end
 end
+
+@testset "Dirichlet rand Inf and NaN (#1702)" begin
+    for d in [
+        Dirichlet([8e-5, 1e-5, 2e-5]),
+        Dirichlet([8e-4, 1e-4, 2e-4]),
+        Dirichlet([4.5e-5, 8e-5]),
+        Dirichlet([6e-5, 2e-5, 3e-5, 4e-5, 5e-5]),
+        Dirichlet(FillArrays.Fill(1e-5, 5))
+    ]
+        x = rand(d, 10^6)
+        @test mean(x, dims = 2) ≈ mean(d) atol=0.01
+        @test var(x, dims = 2) ≈ var(d) atol=0.01
+    end
+
+    for (d, μ) in [ # Subnormal params cause mean(d) to error
+        
+        (Dirichlet([5e-310, 5e-310, 5e-310]), [1/3, 1/3, 1/3]),
+        (Dirichlet(FillArrays.Fill(5e-310, 3)), [1/3, 1/3, 1/3]),
+        (Dirichlet([5e-321, 1e-321, 4e-321]), [.5, .1, .4]),
+        (Dirichlet([1e-321, 2e-321, 3e-321, 4e-321]), [.1, .2, .3, .4]),
+        (Dirichlet(FillArrays.Fill(1e-321, 4)), [.25, .25, .25, .25])
+    ]
+        x = rand(d, 10^6)
+        @test mean(x, dims = 2) ≈ μ atol=0.01
+    end
+end
\ No newline at end of file