diff --git a/Project.toml b/Project.toml
index 3567d7606..30d1bf1e8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "Mooncake"
 uuid = "da2b9cff-9c12-43a0-ae48-6db2b0edb7d6"
 authors = ["Will Tebbutt, Hong Ge, and contributors"]
-version = "0.4.18"
+version = "0.4.19"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
diff --git a/src/interpreter/s2s_reverse_mode_ad.jl b/src/interpreter/s2s_reverse_mode_ad.jl
index a79fed05b..ebc7592a3 100644
--- a/src/interpreter/s2s_reverse_mode_ad.jl
+++ b/src/interpreter/s2s_reverse_mode_ad.jl
@@ -387,23 +387,22 @@ function make_ad_stmts!(stmt::PiNode, line::ID, info::ADInfo)
     # unit test for this, but integration testing seems to catch it in multiple places.
     stmt == PiNode(nothing, Union{}) && return ad_stmt_info(line, nothing, stmt, nothing)
 
-    # Assume that the PiNode contains active data -- it's hard to see why a PiNode would be
-    # created for e.g. a constant. Error if code is encountered where this doesn't hold.
-    is_active(stmt.val) || unhandled_feature("PiNode: $stmt")
-
-    # Get the primal type of this line, and the rdata refs for the `val` of this `PiNode`
-    # and this line itself.
-    P = get_primal_type(info, line)
-    val_rdata_ref_id = get_rev_data_id(info, stmt.val)
-    output_rdata_ref_id = get_rev_data_id(info, line)
-
-    # Assemble the above lines and construct reverse-pass.
-    return ad_stmt_info(
-        line,
-        nothing,
-        PiNode(__inc(stmt.val), fcodual_type(_type(stmt.typ))),
-        Expr(:call, __pi_rvs!, P, val_rdata_ref_id, output_rdata_ref_id),
-    )
+    if is_active(stmt.val)
+        # Get the primal type of this line, and the rdata refs for the `val` of this
+        # `PiNode` and this line itself.
+        P = get_primal_type(info, line)
+        val_rdata_ref_id = get_rev_data_id(info, stmt.val)
+        output_rdata_ref_id = get_rev_data_id(info, line)
+        fwds = PiNode(__inc(stmt.val), fcodual_type(_type(stmt.typ)))
+        rvs = Expr(:call, __pi_rvs!, P, val_rdata_ref_id, output_rdata_ref_id)
+    else
+        # If the value of the PiNode is a constant / QuoteNode etc, then there is nothing to
+        # do on the reverse-pass.
+        fwds = PiNode(const_codual(stmt.val, info), fcodual_type(_type(stmt.typ)))
+        rvs = nothing
+    end
+
+    return ad_stmt_info(line, nothing, fwds, rvs)
 end
 
 @inline function __pi_rvs!(::Type{P}, val_rdata_ref::Ref, output_rdata_ref::Ref) where {P}
diff --git a/test/integration_testing/distributions.jl b/test/integration_testing/distributions.jl
index 72ba86908..79bbbf288 100644
--- a/test/integration_testing/distributions.jl
+++ b/test/integration_testing/distributions.jl
@@ -227,16 +227,22 @@ _pdmat(A) = PDMat(_sym(A) + 5I)
         ),
         (
             :none,
-            "allocs Normal",
+            "truncated Normal",
             (a, b, x) -> logpdf(truncated(Normal(), a, b), x),
             (-0.3, 0.3, 0.1),
         ),
         (
             :none,
-            "allocs Uniform",
+            "truncated Uniform",
             (a, b, α, β, x) -> logpdf(truncated(Uniform(α, β), a, b), x),
             (0.1, 0.9, -0.1, 1.1, 0.4),
         ),
+        (
+            :none,
+            "left-truncated Beta",
+            (a, α, β, x) -> logpdf(truncated(Beta(α, β), lower=a), x),
+            (0.1, 1.1, 1.3, 0.4),
+        ),
         (:none, "Dirichlet", (a, x) -> logpdf(Dirichlet(a), [x, 1-x]), ([1.5, 1.1], 0.6)),
         (
             :none,
diff --git a/test/interpreter/s2s_reverse_mode_ad.jl b/test/interpreter/s2s_reverse_mode_ad.jl
index 4e79b3ec6..263b1b040 100644
--- a/test/interpreter/s2s_reverse_mode_ad.jl
+++ b/test/interpreter/s2s_reverse_mode_ad.jl
@@ -137,11 +137,34 @@ end
                 stmt_info = make_ad_stmts!(PiNode(nothing, Union{}), line, info)
                 @test stmt_info isa ADStmtInfo
             end
-            @testset "unhandled case" begin
-                @test_throws(
-                    Mooncake.UnhandledLanguageFeatureException,
-                    make_ad_stmts!(PiNode(5.0, Float64), ID(), info),
-                )
+            @testset "π (nothing, Nothing)" begin
+                stmt_info = make_ad_stmts!(PiNode(nothing, Nothing), id_line_1, info)
+                @test stmt_info isa ADStmtInfo
+                fwds_stmt = only(stmt_info.fwds)[2].stmt
+                @test fwds_stmt isa PiNode
+                @test fwds_stmt.val == CoDual(nothing, NoFData())
+                @test fwds_stmt.typ == CoDual{Nothing, NoFData}
+                @test only(stmt_info.rvs)[2].stmt === nothing
+            end
+            @testset "π (nothing, CC.Const(nothing))" begin
+                node = PiNode(nothing, CC.Const(nothing))
+                stmt_info = make_ad_stmts!(node, id_line_1, info)
+                @test stmt_info isa ADStmtInfo
+                fwds_stmt = only(stmt_info.fwds)[2].stmt
+                @test fwds_stmt isa PiNode
+                @test fwds_stmt.val == CoDual(nothing, NoFData())
+                @test fwds_stmt.typ == CoDual{Nothing, NoFData}
+                @test only(stmt_info.rvs)[2].stmt === nothing
+            end
+            @testset "π (GlobalRef, Type)" begin
+                node = PiNode(GlobalRef(S2SGlobals, :const_float), Any)
+                stmt_info = make_ad_stmts!(node, id_line_1, info)
+                @test stmt_info isa ADStmtInfo
+                fwds_stmt = only(stmt_info.fwds)[2].stmt
+                @test fwds_stmt isa PiNode
+                @test fwds_stmt.val == CoDual(5.0, NoFData())
+                @test fwds_stmt.typ == CoDual
+                @test only(stmt_info.rvs)[2].stmt === nothing
             end
             @testset "sharpen type of ID" begin
                 line = id_line_1